testbookLayout.git

			@@ -1,818 +1,2168 @@
			<template>
			<div class="chapter" num="2">
			<div class="page-box" page="4">
			<div v-if="showPageList.indexOf(4) > -1">
			<div class="chapter" num="1">
			<div class="page-box" page="8">
			<div v-if="showPageList.indexOf(8) > -1">
			<h1 id="a007">
			<img class="img-0" alt="" src="../../assets/images/dy3.jpg" />
			<img class="img-0" alt="" src="../../assets/images/dy1.jpg" />
			</h1>
			<div class="padding-116">
			<p>
			在客观世界中存在各种各样的运动变化现象.如搭载神舟十四号载人飞船的长征二号运载火箭发射过程中，飞船与发射点距离会随着时间的变化而变化；深海勇士号载人潜水器在下潜实验过程中，其压强随着下潜深度的增加而增大；代表新能源技术的光伏发电和风能发电，我国的装机容量随时间变化而增长；我国快速发展的高速铁路，其总里程是逐年增加的，现已突破4万km
			，稳居世界第一；每个人的体温随着时间的变化而变化；到商店购买同一种饮料的数量越多，付费越多等.这些动态变化现象都表现为变量之间的对应关系，我们常用函数模型来描述这些变量之间的关系和规律，并通过研究函数来认识客观世界.
			如期实现建军一百年奋斗目标，加快把人民军队建成世界一流军队，是全面建设社会主义现代化的战略要求.其中，武器装备现代化是军队现代化的重点之一.在2019年10月1日举行的中华人民共和国成立70周年的阅兵式上，共出现32个装备方队.根据各种装备的功能，可以将这32个装备方队分成7个模块，例如，战旗方队、坦克方队、轻型装甲方队、两栖突击车方队等9个方队组成了陆上作战模块；岸舰导弹方队、舰舰/潜舰导弹方队和舰载防空武器方队组成了海上作战模块；预警雷达方队、地空导弹第一方队、地空导弹第二方队和野战防空导弹方队组成了防空反导模块等.
			</p>
			<p>
			函数是描述客观世界变化规律和解决数学问题的重要工具.它与代数式、方程、不等式等知识联系紧密，是进一步学习数学的重要基础.函数的概念及其反映的数学思想和方法已广泛渗透到数学的各个领域，并在现实生活中有着广泛的应用.
			我们还可以列出更多关于阅兵式的重要信息，借助集合的思想和方法可以解决相关问题，这是本单元将要学习的内容.
			</p>
			<p>
			本单元主要学习函数的概念、函数的表示方法、函数的单调性和奇偶性以及函数的应用.本单元的学习，重在感受用直观想象从具体问题中抽象出数学问题，并用精确的数学符号语言表达概念、性质、推理等；掌握研究函数的基本内容、过程和方法；运用建立分段函数、二次函数等数学模型解决实际问题的方法；积累一定的数学经验和方法，提升直观想象、数学抽象、数学建模、逻辑推理等核心素养.
			</p>
			</div>
			</div>
			</div>
			<div class="page-box" page="5">
			<div v-if="showPageList.indexOf(5) > -1">
			<div class="padding-116">
			<p class="left">
			<img class="inline2" alt="" src="../../assets/images/xxmb.jpg" />
			</p>
			<div class="fieldset">
			<p>1.函数的概念.</p>
			<p>
			能从具体情境中抽象概括出函数的概念，学习用集合语言和对应关系描述函数概念.
			</p>
			<p>2.函数的表示方法.</p>
			<p>了解函数的三种表示方法，会恰当地选用这些方法表示函数；</p>
			<p>理解分段函数的概念；</p>
			<p>通过研究函数的变化规律来把握客观世界中事物的变化规律.</p>
			<p>3.函数的单调性和奇偶性.</p>
			<p>
			学习用精准的数学符号语言描述函数的性质，掌握判断函数单调性和奇偶性的方法.
			</p>
			<p>4.函数的应用.</p>
			<p>初步掌握建立分段函数、二次函数模型来解决实际问题的方法；</p>
			<p>能运用函数的思想和方法解决实际问题，提升核心素养和思维品质.</p>
			</div>
			</div>
			</div>
			</div>
			<div class="page-box" page="6">
			<div v-if="showPageList.indexOf(6) > -1">
			<ul class="page-header-box">
			<li>
			<p>第三单元函数</p>
			</li>
			<li>
			<p><span>089</span></p>
			</li>
			</ul>
			<div class="padding-116">
			<h3 id="c031">
			3.3.2 函数的奇偶性<span class="fontsz2">＞＞＞</span>
			</h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/wttc.jpg" />
			集合论是现代数学的一个重要基础，很多数学分支都是建立在集合论的基础上的.由于集合语言简明准确，有利于迅速、快捷地思考，清晰简洁地表述问题，因此它在人们的日常生活和生产实践中得到了较广泛的应用.
			</p>
			<p>
			函数<i>f</i>（<i>x</i>）=\|<i>x</i>\|和<i>g</i>（<i>x</i>）=<i>x</i
			><sup>2</sup>的图像的对称性如何？
			本单元主要学习集合的初步知识，包括集合及其表示、集合之间的关系、集合的运算等.通过本单元的学习，你们将能更好地理解初中学过的数学知识内容，更好地理解数学中的集合语言.尝试运用集合语言简洁地表述数学中的问题，学会运用集合的思想方法研究和解决这些数学问题，有助于你们提升数学运算、直观想象、逻辑推理和数学抽象等核心素养，并为你们进一步学习数学奠定扎实的基础.
			</p>
			<textarea
			cols="30"
			rows="4"
			v-model="chapterData.txtOne"
			placeholder="请输入内容"
			class="w100 ta-br textarea-text"
			@input="handleChapterData"
			></textarea>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/tjfx.jpg" />
			</p>
			<p>
			列出表3-11和表3-12，画出函数<i>f</i>（<i>x</i>）=\|<i>x</i>\|
			和<i>g</i>（<i>x</i>）=<i>x</i><sup>2</sup>的图像，如图3-14（1）
			和（2）所示.
			</p>
			<p class="img">表3-11</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0100-1.jpg" />
			</p>
			<p class="img">表3-12</p>
			<p class="center">
			<img class="img-a" alt="" src="../../assets/images/0100-2.jpg" />
			</p>
			<iframe
			src="https://www.geogebra.org/calculator"
			frameborder="0"
			class="iframe-box"
			></iframe>
			<p class="center openImgBox">
			<img class="img-c" alt="" src="../../assets/images/0100-3.jpg" />
			</p>
			<p class="img">图3-14</p>
			<p>
			观察图3-14（1）
			发现，函数<i>f</i>（<i>x</i>）=\|<i>x</i>\|的定义域是（-∞，+∞），函数图像关于<i>y</i>轴对称.从表3-11中还发现，当自变量取一对相反数时，对应的函数值相等，如<i>f</i>（-1）=<i>f</i>（1）=1，<i>f</i>（-2）=<i>f</i>（2）=2，<i>f</i>（-3）=<i>f</i>（3）=3，…实际上，对任意<i>x</i>∈（-∞，+∞），都有<i>f</i>（-<i>x</i>）=\|-<i>x</i>\|=\|<i>x</i>\|=<i>f</i>（<i>x</i>），即<i>f</i>（-<i>x</i>）=<i>f</i>（<i>x</i>）.
			</p>
			<p>
			图3-14（2）中，函数<i>g</i>（<i>x</i>）=<i>x</i
			><sup>2</sup
			>的定义域是（-∞，+∞），函数图像也关于<i>y</i>轴对称.表3-12中，当自变量取一对相反数时，对应的函数值相等，如<i>g</i>（-1）=<i>g</i>（1）=1，<i>g</i>（-2）=<i>g</i>（2）=4，<i>g</i>（-3）=<i>g</i>（3）=9，…实际上，对任意<i>x</i>∈（-∞，+∞），都有<i>g</i>（-<i>x</i>）=（-<i>x</i>）<sup>2</sup>=<i
			>x</i
			><sup>2</sup
			>=<i>g</i>（<i>x</i>），即<i>g</i>（-<i>x</i>）=<i>g</i>（<i>x</i>）.
			</p>
			<p>
			这两个函数的图像都关于 <i>y</i> 轴对称；当自变量取定义域中任意一对相
			</p>
			</div>
			</div>
			</div>
			<div class="page-box" page="7">
			<div v-if="showPageList.indexOf(7) > -1">
			<ul class="page-header-odd fl al-end">
			<li>090</li>
			<li>数学.基础模块</li>
			<li></li>
			</ul>
			<div class="padding-116">
			<p class="t0">反数时，对应的函数值都相等，这种函数就是偶函数.</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>
			一般地，设函数<i>f</i>（<i>x</i>）的定义域为<i>D</i>，如果对于<span
			class="u"
			>任意</span
			><i>x</i>∈<i>D</i>，<span class="u">都有</span
			>-<i>x</i>∈<i>D</i>，且<i>f</i>（-<i>x</i>）=<i>f</i>（<i>x</i>），那么函数<i>f</i>（<i>x</i>）就叫作<b>偶函数</b>，如图3-15所示.<b>偶函数的图像关于<i>y</i>轴对称</b>.
			</p>
			<p>
			我们可以由函数的图像是否关于<i>y</i>轴对称来判断函数是不是偶函数.
			</p>
			<p class="center openImgBox">
			<img
			class="img-c"
			alt=""
			src="../../assets/images/0101-1.jpg"
			style="width: 40%"
			/>
			</p>
			<p class="img fl fl-cn ju-cn">
			<span>图3-15</span>
			<el-tooltip
			class="item"
			effect="dark"
			:content="chapterData.isCollectImg ? '点击取消' : '点击收藏'"
			placement="top-start"
			>
			<img
			:src="collectResourceList.findIndex(item => item.id == '722FE833') > -1 ? collectCheck : collectImg"
			alt=""
			class="collect-btn"
			@click="handleCollect('img')"
			/>
			</el-tooltip>
			</p>
			<video
			:src="videoPath"
			webkit-playsinline="true"
			x-webkit-airplay="true"
			playsinline="true"
			x5-video-orientation="h5"
			x5-video-player-fullscreen="true"
			x5-playsinline=""
			controls
			controlslist="nodownload"
			class="video-border w100"
			></video>
			<p class="img fl fl-cn ju-cn">
			<span>视频：判数函数奇偶性的方法和步骤 </span>
			<el-tooltip
			class="item"
			effect="dark"
			:content="chapterData.isCollectVideo ? '点击取消' : '点击收藏'"
			placement="top-start"
			>
			<img
			:src="collectResourceList.findIndex(item => item.id == 'a28cd862d61b5df2201406b76e9f01b0') > -1 ? collectCheck : collectImg"
			alt=""
			class="collect-btn"
			@click="handleCollect('video')"
			/>
			</el-tooltip>
			</p>
			<p class="fl">
			<span>
			<span class="zt-ls"><b>例1</b></span
			>　根据图3-16中函数的图像，判断哪些函数是偶函数.
			</span>
			<span class="btn-box" @click="isShowExampleOne = !isShowExampleOne">
			<svg
			xmlns="http://www.w3.org/2000/svg"
			width="16.501"
			height="16.501"
			viewBox="0 0 20.501 20.501"
			>
			<path
			class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)"
			/>
			</svg>
			</span>
			</p>
			<p class="center openImgBox">
			<img class="img-c" alt="" src="../../assets/images/0101-2.jpg" />
			</p>
			<p class="img">图3-16</p>
			<div v-if="isShowExampleOne">
			<p>
			<span class="zt-ls"><b>解</b></span> 在四个函数图像中，图3-16（1）
			和图3-16（4）的函数图像关于<i>y</i>轴对称；图3-16（2）
			和图3-16（3）
			的函数图像不关于<i>y</i>轴对称.根据偶函数的图像具有关于<i>y</i>轴对称的特点，图3-16（1）和图3-16（4）的函数是偶函数，图3-16（2）和图3-16（3）的函数不是偶函数.
			</p>
			</div>
			</div>
			</div>
			</div>
			<div class="page-box" page="8">
			<div v-if="showPageList.indexOf(8) > -1">
			<ul class="page-header-box">
			<li>
			<p>第三单元函数</p>
			</li>
			<li>
			<p><span>091</span></p>
			</li>
			</ul>
			<div class="padding-116">
			<p class="fl">
			<span>
			<span class="zt-ls"><b>例2</b></span>
			已知<i>f</i>（<i>x</i>）=\|<i>x</i>\|+1图像在<i>y</i>轴右边的部分如图3-17所示.试画出这个函数图像在<i>y</i>轴左边的部分.
			</span>
			<span class="btn-box" @click="isShowExampleTwo = !isShowExampleTwo">
			<svg
			xmlns="http://www.w3.org/2000/svg"
			width="16.501"
			height="16.501"
			viewBox="0 0 20.501 20.501"
			>
			<path
			class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)"
			/>
			</svg>
			</span>
			</p>
			<p class="center openImgBox">
			<img
			class="img-c"
			alt=""
			src="../../assets/images/0102-1.jpg"
			style="width: 40%"
			/>
			</p>
			<p class="img">图3-17</p>
			<p v-if="isShowExampleTwo">
			<span class="zt-ls"><b>解</b></span>
			函数<i>f</i>（<i>x</i>）=\|<i>x</i>\|+1的定义域是（-∞，+∞），因为它是偶函数，所以根据其图像关于<i>y</i>轴对称的特点，即可画出这个函数在<i>x</i>∈（-∞，0］上的图像.
			</p>
			<p>
			如图3-18所示，在<i>y</i>轴右边的图像上取两点<i>A</i>和<i>B</i>，分别画出它们关于<i>y</i>轴对称的点<i>A</i>′和<i>B</i>′，然后连线<i>A</i>′<i>B</i>′，就得到这个函数的图像在<i>y</i>轴左边的部分.
			</p>
			<p class="center openImgBox">
			<img
			class="img-c"
			alt=""
			src="../../assets/images/0102-2.jpg"
			style="width: 40%"
			/>
			</p>
			<p class="img">图3-18</p>
			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img
			class="img-gn1"
			alt=""
			src="../../assets/images/tbts.jpg"
			/>
			</p>
			</div>
			<p class="block">
			一个函数是不是偶函数，可以由函数的图像是否关于<i>y</i>轴对称来判断；当函数用解析法表示时，可以用偶函数的定义来判断.
			</p>
			</div>
			<p>
			<span class="zt-ls"><b>例3</b></span
			>　判断下列函数是不是偶函数.
			</p>
			<ul>
			<li class="fl fl-cn">
			<p>（1） <i>f</i>（<i>x</i>）=3<i>x</i><sup>2</sup>+1；</p>
			<span
			class="btn-box"
			@click="isShowExampleThree = !isShowExampleThree"
			>
			<svg
			xmlns="http://www.w3.org/2000/svg"
			width="16.501"
			height="16.501"
			viewBox="0 0 20.501 20.501"
			>
			<path
			class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)"
			/>
			</svg>
			</span>
			<span class="btn-box" @click="openThinkingDialog">
			<svg
			xmlns="http://www.w3.org/2000/svg"
			width="16.545"
			height="18.112"
			viewBox="0 0 20.545 22.112"
			>
			<path
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			d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
			transform="translate(-3761 14334.001)"
			/>
			</svg>
			</span>
			<span class="btn-box" @click="stepDialog = true">
			<svg
			xmlns="http://www.w3.org/2000/svg"
			width="15.28"
			height="17.563"
			viewBox="0 0 19.28 20.563"
			>
			<g transform="translate(-109.056 -82.941)">
			<path
			class="a"
			d="M3439.656-15185.7h-12.643a1.815,1.815,0,0,1-1.816-1.81v-16.944a1.83,1.83,0,0,1,1.816-1.809h15.674a1.8,1.8,0,0,1,1.79,1.809v13.93h-4.217a.6.6,0,0,0-.6.6v4.217h0Zm-9.819-2.764a.5.5,0,0,0-.5.5.5.5,0,0,0,.5.5h4a.5.5,0,0,0,.5-.5.5.5,0,0,0-.5-.5Zm0-2a.5.5,0,0,0-.5.5.5.5,0,0,0,.5.5h4a.5.5,0,0,0,.5-.5.5.5,0,0,0-.5-.5Zm1.393-8.525a2.416,2.416,0,0,0-2.416,2.411,2.421,2.421,0,0,0,2.416,2.42h.111a1.8,1.8,0,0,0,1.1,1.1,1.809,1.809,0,0,0,.6.107,1.808,1.808,0,0,0,1.7-1.206h4.072l-.172.172a.635.635,0,0,0-.179.454.569.569,0,0,0,.179.4.637.637,0,0,0,.435.176.6.6,0,0,0,.424-.176l1.2-1.214a.618.618,0,0,0,0-.858l-1.2-1.187a.619.619,0,0,0-.431-.176.6.6,0,0,0-.427.176.615.615,0,0,0,0,.854l.172.176h-4.072a1.8,1.8,0,0,0-1.1-1.1,1.755,1.755,0,0,0-.6-.1,1.808,1.808,0,0,0-1.7,1.206h-.111a.554.554,0,0,1-.145-.016,1.2,1.2,0,0,1-.84-.4,1.217,1.217,0,0,1-.3-.878,1.2,1.2,0,0,1,1.206-1.137.407.407,0,0,1,.069,0h3.729a1.807,1.807,0,0,0,1.118,1.114,1.816,1.816,0,0,0,.576.091,1.789,1.789,0,0,0,1.7-1.205h.309a2.415,2.415,0,0,0,1.679-.775,2.407,2.407,0,0,0,.637-1.729,2.411,2.411,0,0,0-2.419-2.324h-6.213a1.821,1.821,0,0,0-1.107-1.1,1.8,1.8,0,0,0-.6-.1,1.814,1.814,0,0,0-1.706,1.2,1.8,1.8,0,0,0,.077,1.389,1.787,1.787,0,0,0,1.026.92,1.841,1.841,0,0,0,.6.1,1.807,1.807,0,0,0,1.706-1.2h6.266a1.179,1.179,0,0,1,.836.4,1.22,1.22,0,0,1,.305.874,1.213,1.213,0,0,1-1.214,1.146h-.172a1.8,1.8,0,0,0-1.118-1.118,1.711,1.711,0,0,0-.576-.1,1.8,1.8,0,0,0-1.706,1.214Z"
			transform="translate(-3316.14 15289.201)"
			/>
			<path
			class="a"
			d="M316.806,239.727a.6.6,0,1,0,.6-.6A.6.6,0,0,0,316.806,239.727Zm-5.421-4.207a.6.6,0,1,0,.6.6A.587.587,0,0,0,311.385,235.52Zm2.4,8.438a.607.607,0,1,0-.6-.613A.621.621,0,0,0,313.789,243.958Z"
			transform="translate(-196.896 -148.921)"
			/>
			<path
			class="a"
			d="M763.392,793.79l3.262-3.262h-3.262Z"
			transform="translate(-638.661 -690.634)"
			/>
			</g>
			</svg>
			</span>
			<span class="btn-box" @click="openMathDiaolog">
			<svg
			xmlns="http://www.w3.org/2000/svg"
			xmlns:xlink="http://www.w3.org/1999/xlink"
			width="15.323"
			height="15.939"
			viewBox="0 0 18.323 15.939"
			>
			<g transform="translate(-398 -946)">
			<path
			class="a"
			d="M11.985,1.241a.894.894,0,0,1-.242.623.79.79,0,0,1-.6.263.644.644,0,0,1-.547-.229,3.034,3.034,0,0,1-.339-.741A.935.935,0,0,0,10.1.846a.4.4,0,0,0-.291-.1.36.36,0,0,0-.333.18,1.836,1.836,0,0,0-.2.478L8.251,4.753H9.7l-.27.79H8.043l-1.51,4.849a27.9,27.9,0,0,1-1.06,2.93,5.5,5.5,0,0,1-1.316,1.857,3.11,3.11,0,0,1-2.189.755,2.258,2.258,0,0,1-1.455-.409A1.192,1.192,0,0,1,0,14.618a.97.97,0,0,1,.27-.693.894.894,0,0,1,.693-.291.741.741,0,0,1,.693.27,1.815,1.815,0,0,1,.2.693c0,.381.2.575.492.575a.817.817,0,0,0,.693-.478,6.983,6.983,0,0,0,.568-1.469L6,5.543H4.5l.236-.776h1.5l.159-.54a14.548,14.548,0,0,1,.693-2.016A4.544,4.544,0,0,1,8.313.694,2.91,2.91,0,0,1,10.281,0a2.425,2.425,0,0,1,.8.145,1.5,1.5,0,0,1,.693.429.963.963,0,0,1,.236.693Z"
			transform="translate(398 948)"
			/>
			<path
			class="b"
			d="M18.323,5.668a3.505,3.505,0,0,1-.152,1.046H17.36a3.969,3.969,0,0,0,.166-1.06.5.5,0,0,0-.062-.236.27.27,0,0,0-.249-.132.346.346,0,0,0-.229.076c-.069.055-.222.208-.471.471L14.936,7.489a22.329,22.329,0,0,0-1.552,1.621l-1.815,1.974a2.168,2.168,0,0,1-1.385.859c-.492,0-.741-.333-.741-.991a3.575,3.575,0,0,1,.3-1.385h.914a4.766,4.766,0,0,0-.263,1.1c0,.18.048.263.159.263s.242-.111.464-.333l2.147-2.286c-.006-.033,1.525-1.611,1.524-1.6l1.3-1.385a2.078,2.078,0,0,1,1.385-.8.755.755,0,0,1,.776.388,1.9,1.9,0,0,1,.173.776Z"
			transform="translate(398 948)"
			/>
			<path
			class="a"
			d="M14.936,7.489l.693,2.251a5.154,5.154,0,0,0,.236.61c.083.159.18.242.3.242a.82.82,0,0,0,.533-.457,4.849,4.849,0,0,0,.339-.817H17.8a4.849,4.849,0,0,1-.693,1.51,2.813,2.813,0,0,1-.873.852,1.766,1.766,0,0,1-.88.27,1.178,1.178,0,0,1-1.018-.464,4.357,4.357,0,0,1-.623-1.309l-.326-1.067a6.4,6.4,0,0,0-.222-.8L12.747,7c-.083-.27-.152-.478-.2-.6a1.136,1.136,0,0,0-.194-.312.4.4,0,0,0-.284-.118c-.326,0-.6.423-.817,1.261h-.769a6.671,6.671,0,0,1,.6-1.5,3.034,3.034,0,0,1,.81-.873,1.663,1.663,0,0,1,.942-.312,1.344,1.344,0,0,1,1.067.471,3.692,3.692,0,0,1,.644,1.268l.139.436C14.672,6.7,14.936,7.489,14.936,7.489Z"
			transform="translate(398 948)"
			/>
			</g>
			</svg>
			</span>
			</li>
			<li class="fl fl-cn">
			<p>（2） <i>f</i>（<i>x</i>）=<i>x</i><sup>2</sup>+<i>x</i>；</p>
			<span
			class="btn-box"
			@click="isShowExampleFour = !isShowExampleFour"
			>
			<svg
			xmlns="http://www.w3.org/2000/svg"
			width="16.501"
			height="16.501"
			viewBox="0 0 20.501 20.501"
			>
			<path
			class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)"
			/>
			</svg>
			</span>
			<span class="btn-box" @click="openMathDiaolog">
			<svg
			xmlns="http://www.w3.org/2000/svg"
			xmlns:xlink="http://www.w3.org/1999/xlink"
			width="15.323"
			height="15.939"
			viewBox="0 0 18.323 15.939"
			>
			<g transform="translate(-398 -946)">
			<path
			class="a"
			d="M11.985,1.241a.894.894,0,0,1-.242.623.79.79,0,0,1-.6.263.644.644,0,0,1-.547-.229,3.034,3.034,0,0,1-.339-.741A.935.935,0,0,0,10.1.846a.4.4,0,0,0-.291-.1.36.36,0,0,0-.333.18,1.836,1.836,0,0,0-.2.478L8.251,4.753H9.7l-.27.79H8.043l-1.51,4.849a27.9,27.9,0,0,1-1.06,2.93,5.5,5.5,0,0,1-1.316,1.857,3.11,3.11,0,0,1-2.189.755,2.258,2.258,0,0,1-1.455-.409A1.192,1.192,0,0,1,0,14.618a.97.97,0,0,1,.27-.693.894.894,0,0,1,.693-.291.741.741,0,0,1,.693.27,1.815,1.815,0,0,1,.2.693c0,.381.2.575.492.575a.817.817,0,0,0,.693-.478,6.983,6.983,0,0,0,.568-1.469L6,5.543H4.5l.236-.776h1.5l.159-.54a14.548,14.548,0,0,1,.693-2.016A4.544,4.544,0,0,1,8.313.694,2.91,2.91,0,0,1,10.281,0a2.425,2.425,0,0,1,.8.145,1.5,1.5,0,0,1,.693.429.963.963,0,0,1,.236.693Z"
			transform="translate(398 948)"
			/>
			<path
			class="b"
			d="M18.323,5.668a3.505,3.505,0,0,1-.152,1.046H17.36a3.969,3.969,0,0,0,.166-1.06.5.5,0,0,0-.062-.236.27.27,0,0,0-.249-.132.346.346,0,0,0-.229.076c-.069.055-.222.208-.471.471L14.936,7.489a22.329,22.329,0,0,0-1.552,1.621l-1.815,1.974a2.168,2.168,0,0,1-1.385.859c-.492,0-.741-.333-.741-.991a3.575,3.575,0,0,1,.3-1.385h.914a4.766,4.766,0,0,0-.263,1.1c0,.18.048.263.159.263s.242-.111.464-.333l2.147-2.286c-.006-.033,1.525-1.611,1.524-1.6l1.3-1.385a2.078,2.078,0,0,1,1.385-.8.755.755,0,0,1,.776.388,1.9,1.9,0,0,1,.173.776Z"
			transform="translate(398 948)"
			/>
			<path
			class="a"
			d="M14.936,7.489l.693,2.251a5.154,5.154,0,0,0,.236.61c.083.159.18.242.3.242a.82.82,0,0,0,.533-.457,4.849,4.849,0,0,0,.339-.817H17.8a4.849,4.849,0,0,1-.693,1.51,2.813,2.813,0,0,1-.873.852,1.766,1.766,0,0,1-.88.27,1.178,1.178,0,0,1-1.018-.464,4.357,4.357,0,0,1-.623-1.309l-.326-1.067a6.4,6.4,0,0,0-.222-.8L12.747,7c-.083-.27-.152-.478-.2-.6a1.136,1.136,0,0,0-.194-.312.4.4,0,0,0-.284-.118c-.326,0-.6.423-.817,1.261h-.769a6.671,6.671,0,0,1,.6-1.5,3.034,3.034,0,0,1,.81-.873,1.663,1.663,0,0,1,.942-.312,1.344,1.344,0,0,1,1.067.471,3.692,3.692,0,0,1,.644,1.268l.139.436C14.672,6.7,14.936,7.489,14.936,7.489Z"
			transform="translate(398 948)"
			/>
			</g>
			</svg>
			</span>
			</li>
			<li class="fl fl-cn">
			<p>（3） <i>f</i>（<i>x</i>）=5<i>x</i>+2.</p>
			<span
			class="btn-box"
			@click="isShowExampleFive = !isShowExampleFive"
			>
			<svg
			xmlns="http://www.w3.org/2000/svg"
			width="16.501"
			height="16.501"
			viewBox="0 0 20.501 20.501"
			>
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			class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)"
			/>
			</svg>
			</span>
			<span class="btn-box" @click="openMathDiaolog">
			<svg
			xmlns="http://www.w3.org/2000/svg"
			xmlns:xlink="http://www.w3.org/1999/xlink"
			width="15.323"
			height="15.939"
			viewBox="0 0 18.323 15.939"
			>
			<g transform="translate(-398 -946)">
			<path
			class="a"
			d="M11.985,1.241a.894.894,0,0,1-.242.623.79.79,0,0,1-.6.263.644.644,0,0,1-.547-.229,3.034,3.034,0,0,1-.339-.741A.935.935,0,0,0,10.1.846a.4.4,0,0,0-.291-.1.36.36,0,0,0-.333.18,1.836,1.836,0,0,0-.2.478L8.251,4.753H9.7l-.27.79H8.043l-1.51,4.849a27.9,27.9,0,0,1-1.06,2.93,5.5,5.5,0,0,1-1.316,1.857,3.11,3.11,0,0,1-2.189.755,2.258,2.258,0,0,1-1.455-.409A1.192,1.192,0,0,1,0,14.618a.97.97,0,0,1,.27-.693.894.894,0,0,1,.693-.291.741.741,0,0,1,.693.27,1.815,1.815,0,0,1,.2.693c0,.381.2.575.492.575a.817.817,0,0,0,.693-.478,6.983,6.983,0,0,0,.568-1.469L6,5.543H4.5l.236-.776h1.5l.159-.54a14.548,14.548,0,0,1,.693-2.016A4.544,4.544,0,0,1,8.313.694,2.91,2.91,0,0,1,10.281,0a2.425,2.425,0,0,1,.8.145,1.5,1.5,0,0,1,.693.429.963.963,0,0,1,.236.693Z"
			transform="translate(398 948)"
			/>
			<path
			class="b"
			d="M18.323,5.668a3.505,3.505,0,0,1-.152,1.046H17.36a3.969,3.969,0,0,0,.166-1.06.5.5,0,0,0-.062-.236.27.27,0,0,0-.249-.132.346.346,0,0,0-.229.076c-.069.055-.222.208-.471.471L14.936,7.489a22.329,22.329,0,0,0-1.552,1.621l-1.815,1.974a2.168,2.168,0,0,1-1.385.859c-.492,0-.741-.333-.741-.991a3.575,3.575,0,0,1,.3-1.385h.914a4.766,4.766,0,0,0-.263,1.1c0,.18.048.263.159.263s.242-.111.464-.333l2.147-2.286c-.006-.033,1.525-1.611,1.524-1.6l1.3-1.385a2.078,2.078,0,0,1,1.385-.8.755.755,0,0,1,.776.388,1.9,1.9,0,0,1,.173.776Z"
			transform="translate(398 948)"
			/>
			<path
			class="a"
			d="M14.936,7.489l.693,2.251a5.154,5.154,0,0,0,.236.61c.083.159.18.242.3.242a.82.82,0,0,0,.533-.457,4.849,4.849,0,0,0,.339-.817H17.8a4.849,4.849,0,0,1-.693,1.51,2.813,2.813,0,0,1-.873.852,1.766,1.766,0,0,1-.88.27,1.178,1.178,0,0,1-1.018-.464,4.357,4.357,0,0,1-.623-1.309l-.326-1.067a6.4,6.4,0,0,0-.222-.8L12.747,7c-.083-.27-.152-.478-.2-.6a1.136,1.136,0,0,0-.194-.312.4.4,0,0,0-.284-.118c-.326,0-.6.423-.817,1.261h-.769a6.671,6.671,0,0,1,.6-1.5,3.034,3.034,0,0,1,.81-.873,1.663,1.663,0,0,1,.942-.312,1.344,1.344,0,0,1,1.067.471,3.692,3.692,0,0,1,.644,1.268l.139.436C14.672,6.7,14.936,7.489,14.936,7.489Z"
			transform="translate(398 948)"
			/>
			</g>
			</svg>
			</span>
			</li>
			</ul>
			<div v-if="isShowExampleThree">
			<p>
			<span class="zt-ls"><b>解</b></span
			>（1）函数<i>f</i>（<i>x</i>）=3<i>x</i
			><sup>2</sup
			>+1的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<b>R</b>，
			</p>
			<p>而</p>
			<p class="center">
			<i>f</i>（-<i>x</i>）=3（-<i>x</i>）<sup>2</sup>+1=3<i>x</i
			><sup>2</sup>+1=<i>f</i>（<i>x</i>），
			</p>
			<p>
			所以，函数<i>f</i>（<i>x</i>）=3<i>x</i><sup>2</sup>+1是偶函数.
			</p>
			</div>
			<div v-if="isShowExampleFour">
			<p>
			（2）函数<i>f</i>（<i>x</i>）=<i>x</i
			><sup>2</sup
			>+<i>x</i>的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<b>R</b>，而
			</p>
			<p class="center">
			<i>f</i>（-<i>x</i>）=（-<i>x</i>）<sup>2</sup>+（-<i>x</i>）=<i
			>x</i
			><sup>2</sup>-<i>x</i>≠<i>f</i>（<i>x</i>），
			</p>
			<p>
			所以，函数<i>f</i>（<i>x</i>）=<i>x</i
			><sup>2</sup>+<i>x</i>不是偶函数.
			</p>
			</div>
			<div v-if="isShowExampleFive">
			<p>
			（3）
			函数<i>f</i>（<i>x</i>）=5<i>x</i>+2的定义域是<b>R</b>，对任意<i>x</i>∈<b>R</b>，都有-<i>x</i>∈<i>R</i>，而
			</p>
			<p class="center">
			<i>f</i
			>（-<i>x</i>）=5（-<i>x</i>）+2=-5<i>x</i>+2≠<i>f</i>（<i>x</i>），
			</p>
			<p>所以，函数<i>f</i>（<i>x</i>）=5<i>x</i>+2不是偶函数.</p>
			</div>
			<div class="bk-hzjl">
			<div class="bj1-hzjl">
			<p class="left">
			<img
			class="img-gn2"
			alt=""
			src="../../assets/images/hzjl.jpg"
			/>
			</p>
			</div>
			<p class="block tl">
			如果<i>f</i>（<i>x</i>），<i>g</i>（<i>x</i>）都是定义域为<i>D</i>的偶函数，那么<i>f</i>（<i>x</i>）+<i>g</i>（<i>x</i>）和<i>f</i>（<i>x</i>）<i>g</i>（<i>x</i>）仍是偶函数吗？
			<textarea
			cols="30"
			rows="4"
			v-model="chapterData.txtTwo"
			placeholder="请输入内容"
			class="w100 ta-br textarea-text"
			@input="handleChapterData"
			></textarea>
			</p>
			</div>
			</div>
			</div>
			</div>
			<div class="page-box" page="9">
			<div v-if="showPageList.indexOf(9) > -1">
			<div class="padding-116">
			<p class="left">
			<img class="inline2" alt="" src="../../assets/images/xxmb.jpg" />
			</p>
			<div class="fieldset">
			<p>1.集合及其表示.</p>
			<p>
			了解集合的概念；理解元素与集合之间的关系；了解空集、有限集和无限集的含义；掌握常用数集的表示符号，初步掌握列举法和描述法等集合的表示方法.
			</p>
			<p>2.集合之间的关系.</p>
			<p>
			理解集合之间包含与相等、子集与真子集的含义；掌握集合之间基本关系的符号表示.
			</p>
			<p>3.集合的运算.</p>
			<p>理解两个集合的交集、并集；了解全集和补集的含义.</p>
			</div>
			</div>
			</div>
			</div>
			<!-- 003 -->
			<div class="page-box" page="10">
			<div v-if="showPageList.indexOf(10) > -1">
			<ul class="page-header-box">
			<li>
			<p>第一单元集合</p>
			</li>
			<li>
			<p><span>003</span></p>
			</li>
			</ul>
			<div class="padding-116">
			<h2 id="c031">1.1 集合及其表示<span class="fontsz2">＞＞＞</span></h2>

			<h3>1.1.1 集合与元素<span class="fontsz2">＞＞＞</span></h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/gcsk.jpg" />
			</p>

			<span> 观察几组对象： </span>
			<p>
			（1）中华人民共和国成立70周年阅兵式上的海上作战模块包括的所有方队；
			</p>
			<p>（2） 0～10中的所有奇数；</p>
			<p>（3）我国农历二十四节气；</p>
			<p>（4）方程x2-5x-6=0的解；</p>
			<p>（5）到一个角的两边距离相等的所有点.</p>

			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>

			<p>
			（1）
			中的所有对象是岸舰导弹方队、舰舰/潜舰导弹方队和舰载防空武器方队；（2）
			中的所有对象是1，3，5，7，9；（3）
			中的所有对象是立春、雨水、惊蛰等二十四节气.类似地，也可以找到（4）
			和（5）中的所有对象.
			</p>

			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/gn.jpg" />
			</p>
			</div>
			<p class="block">集合</p>
			<p class="block">集合与元素</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>

			<p>
			像这样，由一些确定的对象所组成的整体就称为集合（简称集），集合通常用大写字母A，B，C，…表示.
			</p>
			<p>
			集合中的每个确定的对象叫作这个集合的元素.集合中的元素通常用小写字母a，b，c，…表示.
			</p>
			<p>
			如果a是集合A中的元素，就说a属于A，记作a∈A，读作“a属于A”；如果b不是集合A中的元素，就说b不属于A，记作b∉A，读作“b不属于A”.
			</p>

			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" />
			</p>
			</div>
			<p class="block">
			给定一个集合，任何一个对象是否属于这个集合就很明确了.也就是说，给定一个集合，就给定了一个明确的条件，据此可以判定任何一个对象是否属于这个集合.这说明集合的元素具有确定性.
			</p>

			<p class="block">
			例如，“大于10的偶数”可以组成一个集合，将其记为集合B，那么集合B中的元素就是12，14，16，18，20，…，则16∈B，17∉B，8∉B.
			</p>

			<p class="block">
			“联合国安全理事会常任理事国”可以组成一个集合，这个集合中的元素是中国、俄罗斯、美国、英国、法国.如果把这个集合记为D，则中国∈D，日本∉D.
			</p>

			<p class="block">
			另外，一个给定集合中的元素不能重复，且在排序上没有顺序要求.也就是说，集合中的元素具有互异性和无序性.
			</p>
			</div>
			</div>
			</div>
			</div>
			<!-- 004 -->
			<div class="page-box" page="11">
			<div v-if="showPageList.indexOf(11) > -1">
			<ul class="page-header-odd fl al-end">
			<li>092</li>
			<li>004</li>
			<li>数学.基础模块</li>
			<li></li>
			<li>上册</li>
			</ul>
			<div class="padding-116">
			<p class="fl" >
			<span class="zt-ls2">例</span>
			<span class="t-" >下列对象能否组成集合？</span>
			<span class="btn-box" @click="openDialog(thinkTwo)">
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			transform="translate(-3761 14334.001)" />
			</svg>
			</span>
			</p>
			<ul>
			<li>
			（1）英文大写字母的全体；
			<span class="btn-box" @click="chapter001.isShowExample1 = !chapter001.isShowExample1">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li>
			<p v-if="chapter001.isShowExample1">
			<span class="zt-ls2">解</span>
			（1）能；
			</p>
			</li>
			<li>
			（2）我们班上高个子同学的全体；
			<span class="btn-box" @click="chapter001.isShowExample2 = !chapter001.isShowExample2">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li>
			<p v-if="chapter001.isShowExample2">
			<span class="zt-ls2">解</span>
			（2）不能；
			</p>
			</li>
			<li>
			（3）不等式2x-7＜0的所有实数解；
			<span class="btn-box" @click="chapter001.isShowExample3 = !chapter001.isShowExample3">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li>
			<p v-if="chapter001.isShowExample3">
			<span class="zt-ls2">解</span>
			（3）能；
			</p>
			</li>
			<li>
			（4）能被5整除的正整数的全体.
			<span class="btn-box" @click="chapter001.isShowExample4 = !chapter001.isShowExample4">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li>
			<p v-if="chapter001.isShowExample4">
			<span class="zt-ls2">解</span>
			（4）能.
			</p>
			</li>
			</ul>
			<p>
			<span class="zt-ls2">分析</span>一些对象是否能够组成集合,要看条件所指的对象是不是确定
			的.不能确定的对象是不能组成集合的.
			</p>
			<div class="bk-hzjl">
			<div class="bj1-hzjl">
			<p class="left">
			<img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
			</p>
			</div>
			<examinations :cardList="questionData[11] ? questionData[11][1] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[11] ? questionData[11][2] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			</div>
			</div>
			</div>
			<!-- 005 -->
			<div class="page-box" page="12">
			<div v-if="showPageList.indexOf(12) > -1">
			<ul class="page-header-box">
			<li>
			<p>第一单元集合</p>
			</li>
			<li>
			<p><span>005</span></p>
			</li>
			</ul>
			<div class="padding-116">
			<h3>1.1.2 常见集合<span class="fontsz2">＞＞＞</span></h3>
			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/gn.jpg" />
			</p>
			</div>
			<p class="block">有限集</p>
			<p class="block">无限集</p>
			<p class="block">空集</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			在上节例（1）
			中，集合中元素的个数是26个，是有限个.像这样元素个数有限的集合，称为<b>有限集</b>.
			</p>
			<p>
			在例（3）（4）
			中，集合中元素的个数有无限多个.像这样元素个数无限的集合，称为
			<b>无限集</b> .
			</p>
			<p>
			还有一种集合，它不含任何元素.例如，方程x2+1=0的实数解组成的集合，因为方程x2+1=0在实数范围内无解，因此，这个集合中没有任何元素.这样的集合叫作
			<b>空集</b> ，记作 ∅.
			</p>

			<div class="bk-hzjl">
			<div class="bj1-hzjl">
			<p class="left">
			<img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
			</p>
			</div>
			<p class="block tl">
			由数字0组成的集合与空集 ∅有区别吗？与同学交流讨论.
			</p>
			</div>

			<p>
			<span class="zt-ls2">例1</span>请指出下列对象中，哪些是有限集，哪些是无限集.
			</p>
			<ul>
			<li>
			（1）某中职学校计算机班上体重50 kg 以上的学生的全体；
			<span class="btn-box" @click="chapter001.isShowExample5 = !chapter001.isShowExample5">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>

			<li v-if="chapter001.isShowExample5">
			<p>
			<span class="zt-ls2">解</span>
			（1）计算机班上体重50 kg
			以上的学生的数量是有限的，所以这是一个有限集.
			</p>
			</li>

			<li>
			（2）方程x2+2x+2=0的所有实数解；
			<span class="btn-box" @click="chapter001.isShowExample6 = !chapter001.isShowExample6">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>

			<li v-if="chapter001.isShowExample6">
			<p>
			<span class="zt-ls2">解</span>
			（2）
			方程x2+2x+2=0没有实数解，这个集合中元素的个数为0.所以这个集合是有限集.
			</p>
			</li>
			<li>
			（3）不等式3-2x＞0的所有实数解.
			<span class="btn-box" @click="chapter001.isShowExample7 = !chapter001.isShowExample7">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>

			<li v-if="chapter001.isShowExample7">
			<p>
			<span class="zt-ls2">解</span>
			（3）不等式3-2x＞0的解集为 { x \| x ＜ 3 2 }
			，包含无限多个实数，所以这个集合是无限集.
			</p>
			</li>
			</ul>

			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/zshg.jpg" />
			</p>
			</div>
			<p class="block">有理数：整数和分数的统称；</p>
			<p class="block">无理数：无限不循环小数；</p>
			<p class="block">实数：有理数和无理数的统称.</p>
			</div>

			<p>
			如果集合中的元素是数，那么这样的集合称为
			<b>数集</b> .在数学中，常用的数集有规定的记号.
			</p>
			</div>
			</div>
			</div>
			<!-- 006 -->
			<div class="page-box" page="13">
			<div v-if="showPageList.indexOf(13) > -1">
			<ul class="page-header-odd fl al-end">
			<li>006</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116">
			<p>全体自然数组成的集合，记作N，称为 <b>自然数集；</b></p>
			<p>全体正整数组成的集合，记作N*或N+，称为； <b>正整数集</b></p>
			<p>全体整数组成的集合，记作Z，称为 <b>整数集；</b></p>
			<p>全体有理数组成的集合，记作Q，称为 <b>有理数集；</b></p>
			<p>全体实数组成的集合，记作R，称为 <b>实数集.</b></p>

			<p><span class="zt-ls2">例2</span>用符号“∈”或“∉”填空.</p>
			<ul>
			<li>
			（1） 1____N+；
			<span class="btn-box" @click="
			chapter001.isShowExample10 = !chapter001.isShowExample10
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample10">
			<p>
			<span class="zt-ls2">解</span>
			（1） 1是正整数，所以填“∈”；
			</p>
			</li>
			<li>
			（2） 3 ；
			<span class="btn-box" @click="
			chapter001.isShowExample11 = !chapter001.isShowExample11
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample11">
			<p>（2） 3 是无理数，不是有理数，所以填“∉”；</p>
			</li>
			<li>
			（3） 1 2 ____Z.
			<span class="btn-box" @click="
			chapter001.isShowExample12 = !chapter001.isShowExample12
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample12">
			<p>（3） 1 2 不是整数，所以填“∉”.</p>
			</li>
			</ul>

			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[13]" :hideCollect="true" sourceType="json" inputBc="#d3edfa" v-if="questionData">
			</examinations>
			</div>
			<h3>1.1.3 集合的表示<span class="fontsz2">＞＞＞</span></h3>
			<p>
			自然数集、正整数集、整数集、有理数集、实数集、空集有特定的符
			号表示, 那么, 一般的集合怎么表示呢?
			</p>
			</div>
			</div>
			</div>
			<!-- 007 -->
			<div class="page-box" page="14">
			<div v-if="showPageList.indexOf(14) > -1">
			<ul class="page-header-box">
			<li>
			<p>第一单元集合</p>
			</li>
			<li>
			<p><span>007</span></p>
			</li>
			</ul>
			<div class="padding-116">
			<p>在集合的表示方法中, 常用的有列举法和描述法.</p>
			<p class="zt-ls2">1.列举法</p>

			<p>
			把集合中的元素一一列举出来，写在大括号内，这种表示集合的方法叫作列举法.
			</p>
			<p>
			例如，
			中华人民共和国成立70周年阅兵式中，装备方队的防空反导模块组成的集合用列举法可以表示为{预警雷达方队，地空导弹第一方队，地空导弹第二方队，野战防空导弹方队}.
			</p>
			<p>小于3的自然数组成的集合用列举法可以表示为{0， 1， 2}.</p>
			<p>由a，b，c三个字母组成的集合用列举法可以表示为{a，b，c}.</p>

			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" />
			</p>
			</div>
			<p class="block">
			例1（2）
			中的集合含有无限多个元素，不需要或不可能一一列举出来，可以依其规律，写出几个元素，用省略号表示其他元素.
			</p>
			</div>

			<p><span class="zt-ls2">例1</span>用列举法表示下列集合.</p>

			<ul>
			<li>
			（1）中国的直辖市组成的集合；
			<span class="btn-box" @click="chapter001.isShowExample8 = !chapter001.isShowExample8">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample8">
			<p>
			<span class="zt-ls2">解</span>（1）
			中国的直辖市组成的集合用列举法可以表示为{北京，天津，上海，重庆}.
			</p>
			</li>
			<li>
			（2）大于10的奇数组成的集合.
			<span class="btn-box" @click="chapter001.isShowExample9 = !chapter001.isShowExample9">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample9">
			<span class="zt-ls2">解</span>
			<p>
			（2）
			大于10的奇数组成的集合用列举法可以表示为{11，13，15，17，19，…}.
			</p>
			</li>
			</ul>

			<p class="zt-ls2">2.描述法</p>

			<p>
			把集合中所有元素的共同特征描述出来，这种表示集合的方法叫作
			<b>描述法.</b>
			</p>

			<p>描述法的一般形式为</p>
			<p>
			{元素的一般符号及取值（或变化）范围\|集合中元素所具有的共同特征}.
			</p>
			<p>例如，由数字1，3，5，7，9组成的集合用描述法可以表示为</p>
			<p>{x∈R\|x 是小于10的正奇数}. ①</p>
			<p>小于3的自然数组成的集合用描述法可以表示为</p>
			<p>{ x ∈ N \| x ＜ 3 }. ②</p>
			<p>方程x2-3x=0的所有实数解组成的集合用描述法可以表示为</p>
			<p>{ x ∈ R \| x 2 − 3 x = 0 } . ③</p>
			<p>
			如果集合中元素x的取值范围是全体实数，则x的取值范围可以省略.例如，①和③中的“∈R”常常省略不写，而分别写成{x\|x是小于10的正奇数}和{x\|x2-3x=0}.
			</p>
			</div>
			</div>
			</div>
			<!-- 008 -->
			<div class="page-box" page="15">
			<div v-if="showPageList.indexOf(15) > -1">
			<ul class="page-header-odd fl al-end">
			<li>008</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116">
			<div style="display: flex; align-items: center">
			<p><span class="zt-ls2">例2</span>用描述法表示下列集合.</p>
			<span class="btn-box" @click="openDialog(thinkThree)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
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			transform="translate(-3761 14334.001)" />
			</svg>
			</span>
			</div>
			<ul>
			<li>
			（1）方程x2-4=0的所有实数解组成的集合；
			<span class="btn-box" @click="
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			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample13">
			<div>
			<p>
			<span class="zt-ls2">解</span>（1）
			方程x2-4=0的所有实数解组成的集合用描述法可以表示为
			</p>

			<p>{x\|x2-4=0}.</p>
			</div>
			</li>
			<li>
			（2）满足1＜x≤3的所有实数x组成的集合；
			<span class="btn-box" @click="
			chapter001.isShowExample14 = !chapter001.isShowExample14
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample14">
			<div>
			<p>（2）满足1＜x≤3的所有实数x组成的集合用描述法可以表示为</p>
			<p>{x\|1＜x≤3}.</p>
			</div>
			</li>
			<li>
			（3）大于10的偶数组成的集合；
			<span class="btn-box" @click="
			chapter001.isShowExample15 = !chapter001.isShowExample15
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample15">
			<div>
			<p>
			（3）
			由于正偶数都能够写成2n（n∈N+）的形式，所以大于10的偶数组成的集合用描述法可以表示为
			</p>
			<p>{x\|x=2n，n＞5，n∈N+}.</p>
			</div>
			</li>
			<li>
			（4）在平面直角坐标系中，一次函数y=-x的图像上所有的点组成的集合.
			<span class="btn-box" @click="
			chapter001.isShowExample16 = !chapter001.isShowExample16
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample16">
			<div>
			<p>
			（4）
			由于平面直角坐标系中的点都可以用坐标写成（x，y）的形式，其中x表示横坐标，y表示纵坐标，所以一次函数y=-x的图像上所有的点组成的集合用描述法可以表示为
			</p>
			<p>{（x，y）\|y=-x}.</p>
			</div>
			</li>
			</ul>

			<p>
			我们把方程或不等式的所有实数解组成的集合叫作该方程或不等式的
			<b>解集</b> .例如，例2（1）和（2）
			中的集合就是方程和不等式的解集.由于解集中的元素是数，因此方程或不等式的解集也是数集.
			</p>

			<p>
			由于数轴上的点与实数是一一对应的，所以实数也可以用数轴上的点来表示.我们把由点组成的集合叫作
			<b>点集</b> .例如，例2（4）
			中的集合就是一个点集，它是由一次函数y=-x的图像上所有的点组成的集合.
			</p>
			<p>
			数集可以用数轴上的点集表示.例2（2）
			中的数集在数轴上的表示如图1-1所示.
			</p>

			<p class="center openImgBox">
			<img class="img-c" alt="" src="../../assets/images/0019-1.jpg" style="width: 40%" />
			</p>
			<p class="img">图1-1</p>

			<p>
			用数轴上的点集来表示数集时，实心的点表示的数属于这一数集，空心的点表示的数不属于这一数集.
			</p>
			</div>
			</div>
			</div>
			<!-- 009 -->
			<div class="page-box" page="16">
			<div v-if="showPageList.indexOf(16) > -1">
			<ul class="page-header-box">
			<li>
			<p>第一单元集合</p>
			</li>
			<li>
			<p><span>009-010</span></p>
			</li>
			</ul>
			<div class="padding-116">
			<div class="bk-hzjl">
			<div class="bj1-hzjl">
			<p class="left">
			<img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
			</p>
			</div>
			<examinations :cardList="questionData[16] ? questionData[16][1] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[16] ? questionData[16][2] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			<h2 id="c031">习题1.1<span class="fontsz2"> ＞＞＞</span></h2>
			<div class="bj">
			<examinations :cardList="questionData[16] ? questionData[16][3] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			<h2 id="c031">
			1.2 集合之间的关系<span class="fontsz2">＞＞＞</span>
			</h2>
			<h3>1.2.1 子集<span class="fontsz2">＞＞＞</span></h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/gcsk.jpg" />
			</p>
			<p>
			我国提出并贯彻新发展理念，着力推进高质量发展，自2012年以来的十年间，我国城镇化率提高11.6%，2021年末城镇化率达到64.7%.若2021年年末全国城镇常住人口组成一个集合A，全国人口组成一个集合B，则集合A与集合B之间有什么关系呢？
			</p>
			</div>
			</div>
			</div>
			<!-- 010 -->
			<div class="page-box hidePage" page="17">
			</div>
			<!-- 011 -->
			<div class="page-box" page="18">
			<div v-if="showPageList.indexOf(18) > -1">
			<ul class="page-header-box">
			<li>
			<p>第一单元集合</p>
			</li>
			<li>
			<p><span>011</span></p>
			</li>
			</ul>
			<div class="padding-116">
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<p>
			我们知道，全国城镇常住人口中的每个人都是全国人口中的一员，因此，集合A中的任何一个元素都是集合B中的元素，这时我们就说集合A与集合B有包含关系.
			</p>
			<p>同样，整数集与有理数集、有理数集与实数集也有包含关系.</p>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>

			<p>
			一般地，对于两个集合A与B，如果集合A中的任何一个元素都是集合B中的元素，即若a∈A，则a∈B，那么称集合A
			<b>包含于</b>集合B，或集合B
			<b>包含</b>集合A，记作A⊆B（或B⊇A），读作“集合A包含于集合B”或“集合B包含集合A”，并称集合A是集合B的
			<b>子集</b>.
			</p>

			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/gn.jpg" />
			</p>
			</div>
			<p class="block">子集</p>
			</div>

			<p>例如，（1）集合A={1}，B={2，3，4}，则A⊈B（或B⊉A）.</p>
			<p>（2）集合A={1，2，3}，B={0，3，5}，则A⊈B（或B⊉A）.</p>
			<p>
			（3）
			集合C={x\|x＞6}，D={x\|x≥-3}，如图1-2所示.若x＞6，则一定有x≥-3，也就是说集合C中的所有元素都属于集合D，所以集合C，D的关系就可以表示为C⊆D（或D⊇C）.
			</p>

			<div class="center openImgBox">
			<img class="img-c" alt="" src="../../assets/images/0022-1.jpg" style="width: 40%" />
			<p class="img" style="font-size: 14px">图1-2</p>
			</div>

			<div class="img-rights openImgBox">
			<img class="img-c" alt="" src="../../assets/images/0022-2.jpg" />
			<p class="img" style="color: #ac92c4; font-size: 14px">图1-3</p>
			</div>
			<p>
			为了直观地表示集合间的关系，我们常用一个封闭的平面几何图形的内部表示集合.这种直观表示集合及其关系的图形，称为Venn图.
			</p>
			<p>如图1-3所示，它直观地表示了集合A是集合B的子集.</p>
			<p>
			当A⊈B，且B⊈A时，它们之间的关系有两种可能，如图1-4（1）（2）所示.
			</p>
			</div>
			</div>
			</div>
			<!-- 012 -->
			<div class="page-box" page="19">
			<div v-if="showPageList.indexOf(19) > -1">
			<ul class="page-header-odd fl al-end">
			<li>012</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116">
			<div class="center openImgBox">
			<img class="img-c" alt="" src="../../assets/images/0023-1.jpg" style="margin-top: 30px" />
			<p class="img" style="font-size: 14px">图1-4</p>
			</div>

			<p>根据子集的定义，任何一个集合A都是它自身的子集，即A⊆A.</p>
			<p>
			我们规定：<b>空集是任何集合的子集</b>
			，即对于任何一个集合A，都有∅⊆A.
			</p>

			<div class="img-float openImgBox">
			<img class="img-c" alt="" src="../../assets/images/0023-2.jpg" />
			<p class="img" style="font-size: 14px">图1-5</p>
			</div>
			<ul>
			<li>
			<div>
			<span
			class="zt-ls2">例1</span>某产品在质量和款式上都合格时，才能被评为合格.若用A表示合格产品的集合，B表示质量合格的产品的集合，C表示款式合格的产品的集合，指出这三个集合之间的包含关系，并指出其中的子集.
			<span class="btn-box" @click="
			chapter001.isShowExample17 = !chapter001.isShowExample17
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</div>
			</li>
			<li v-if="chapter001.isShowExample17">
			<p>
			<span class="zt-ls2">解</span>依题意知，A⊆B，A⊆C.A是B的子集，A也是C的子集.这三个集合之间的包含关系如图1-5所示.
			</p>
			</li>
			<li>
			<span class="zt-ls2">例2</span>写出集合{0，1}的所有子集.
			<span class="btn-box" @click="
			chapter001.isShowExample18 = !chapter001.isShowExample18
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample18">
			<p>
			<span class="zt-ls2">解 </span>
			{0，1}的所有子集是∅，{0}，{1}，{0，1}.
			</p>
			</li>
			</ul>

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			<examinations :cardList="questionData[19][1]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
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			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[19][2]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
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			</div>
			</div>
			<!-- 013 -->
			<div class="page-box" page="20">
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			<ul class="page-header-box">
			<li>
			<p>第一单元集合</p>
			</li>
			<li>
			<p><span>013</span></p>
			</li>
			</ul>
			<div class="padding-116">
			<h3>1.2.2 真子集与相等集合<span class="fontsz2">＞＞＞</span></h3>

			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/wttc.jpg" />
			</p>

			<div class="textIndentation">
			考查下面的集合：
			<p>
			（1）
			某中职学校服装设计班所有学生组成集合M，服装设计班里所有男生组成集合P；
			</p>
			<p>（2）集合A={x\|x2=1}，B={-1，1}.</p>
			<p>集合M与集合P、集合A与集合B有什么关系？</p>
			</div>

			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>

			<p>对于“问题提出”中的（1），显然有P⊆M.</p>
			<p>
			但是服装设计班的女生不属于集合P，也就是说，集合M中有元素不属于集合P.这时候，我们说集合P是集合M的真子集.
			</p>

			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>
			对于两个集合A，B，如果集合A是集合B的子集，且集合B中至少有一个元素不属于集合A，那么集合A叫作集合B的真子集（如图1-6所示），记作A⫋B（或B⫌A），读作“A真包含于B”或“B真包含A”.
			</p>

			<p>例如, 自然数集N是整数集Z的真子集, 即N⫋Z.</p>
			<p>自然数集N也是实数集R的真子集, 即N⫋R</p>
			<p>整数集Z是有理数集Q的真子集, 即Z⫋Q.</p>
			<p>这些集合之间的关系可以用图1-7直观表示.</p>

			<div class="center openImgBox">
			<img class="img-c" alt="" src="../../assets/images/0024-2.jpg" style="width: 50%" />
			<p class="img" style="font-size: 14px">图1-7</p>
			</div>
			<p>
			<b> 空集是任何非空集合的真子集 </b> ，即对任何非空集合A，总有∅⫋A.
			</p>
			<p>例如，因为集合{0} 中有一个元素0，是非空集合，所以∅⫋{0}.</p>
			</div>
			</div>
			</div>
			<!-- 014 -->
			<div class="page-box" page="21">
			<div v-if="showPageList.indexOf(21) > -1">
			<ul class="page-header-odd fl al-end">
			<li>014</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116">
			<ul>
			<li>
			<span class="zt-ls2">例1</span>写出集合 A={a, b, c}的所有子集,
			并说出集合 A 有几个真子集.
			<span class="btn-box" @click="
			chapter001.isShowExample19 = !chapter001.isShowExample19
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>

			<span class="btn-box" @click="openDialog(thinkOne)">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
			<path class="a"
			d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
			transform="translate(-3761 14334.001)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample19">
			<div>
			<p>
			<span class="zt-ls2">解</span>集合A的所有子集是∅，{a}，{b}，{c}，{a，b}，{a，c}，{b，c}，{a，b，c}.
			</p>

			<p>
			除了{a，b，c}外，其他集合都是集合A的真子集，所以集合A有7个真子集.
			</p>
			</div>
			</li>
			</ul>
			<div class="bk-hzjl">
			<div class="bj1-hzjl">
			<p class="left">
			<img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
			</p>
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			<examinations :cardList="questionData[21]" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>

			<p>
			对于“问题提出”中的（2），不难发现集合A和集合B中都只有两个元素-1和1，所以A⊆B，且B⊆A.事实上，这两个集合中的元素是完全相同的，只是这两个集合的表达形式不同.
			</p>

			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>
			一般地，对于两个集合A，B，如果A⊆B，且B⊆A，那么此时集合A与集合B的元素是完全一样的，称集合A与集合B
			<b>相等</b>，记作
			</p>

			<p>A=B.</p>
			<p>
			例如，集合A={x\|x是有两条边相等的三角形}，B={x\|x是等腰三角形}，就有A⊆B，且B⊆A，所以A=B.同样，{x\|x是小于10的正奇数}={1，3，5，7，9}；{x\|x2+5x+6=0}={-2，-3}.
			</p>
			<p>
			这样，真子集还可以理解为：对于集合A，B，如果A⊆B，并且A≠B，就称集合A是集合B的真子集.
			</p>
			</div>
			</div>
			</div>
			<!-- 015 -->
			<div class="page-box" page="22">
			<div v-if="showPageList.indexOf(22) > -1">
			<ul class="page-header-box">
			<li>
			<p>第一单元集合</p>
			</li>
			<li>
			<p><span>015-016</span></p>
			</li>
			</ul>
			<div class="padding-116">
			<p><span class="zt-ls2">例2</span>说出下列每对集合之间的关系.</p>
			<ul>
			<li>
			（1） A={1，2，3，4}和B={1，3，4}；

			<span class="btn-box" @click="
			chapter001.isShowExample20 = !chapter001.isShowExample20
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample20">
			<p><span class="zt-ls2">解</span>（1） A⫌B；</p>
			</li>
			<li>
			（2） P={x\|x＞4}和Q={x\|x＞1}；
			<span class="btn-box" @click="
			chapter001.isShowExample21 = !chapter001.isShowExample21
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample21">
			<p><span class="zt-ls2">解</span>（2） P⫋Q；</p>
			</li>

			<li>
			（3） C={x\|x2+3=0}和 ∅.
			<span class="btn-box" @click="
			chapter001.isShowExample22 = !chapter001.isShowExample22
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample22">
			<p><span class="zt-ls2">解</span>（3） C=∅.</p>
			</li>
			</ul>
			<div class="bk-hzjl">
			<div class="bj1-hzjl">
			<p class="left">
			<img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
			</p>
			</div>
			<examinations :cardList="questionData[22] ? questionData[22][1] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[22] ? questionData[22][2] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			<h2 id="c031">习题1.2<span class="fontsz2"> ＞＞＞</span></h2>
			<div class="bj">
			<examinations :cardList="questionData[22] ? questionData[22][3] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			<h2 id="c031">
			1.3 集合的运算<span class="fontsz2">＞＞＞＞＞＞</span>
			</h2>

			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/gcsk.jpg" />
			</p>

			<div class="img-rights openImgBox">
			<img class="img-c" alt="" src="../../assets/images/0027-1.jpg" />
			<p class="img" style="font-size: 14px">图1-8</p>
			</div>
			<p>
			到2035年，我国要发展成为体育强国.北京市曾在2008年和2022年分别举办了第29届夏季奥运会和第24届冬季奥运会，
			因此成为世界上第一个既举办过夏季奥运会又举办过冬季奥运会的城市.现在用集合的观点来分析这个问题，如图1-8所示，我们用集合U表示世界上所有的城市，用集合A表示到2022年年底举办过夏季奥运会的城市，用集合B表示到2022年年底举办过冬季奥运会的城市.
			</p>
			<p>
			（1）图中哪部分表示既举办过夏季奥运会又举办过冬季奥运会的城市？
			</p>
			<p>
			（2）图中哪部分表示举办过夏季奥运会或者举办过冬季奥运会的城市？
			</p>
			<p>（3）图中哪部分表示没举办过夏季奥运会的城市？</p>
			<p>
			（4）图中哪部分表示既没举办过夏季奥运会又没举办过冬季奥运会的城市？
			</p>
			</div>
			</div>
			</div>
			<!-- 016 -->
			<div class="page-box hidePage" page="23">
			</div>
			<!-- 017 -->
			<div class="page-box" page="24">
			<div v-if="showPageList.indexOf(24) > -1">
			<ul class="page-header-box">
			<li>
			<p>第一单元集合</p>
			</li>
			<li>
			<p><span>017</span></p>
			</li>
			</ul>
			<div class="padding-116">
			<h3>1.3.1 交集<span class="fontsz2">＞＞＞</span></h3>

			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<div class="img-rights openImgBox">
			<img class="img-c" alt="" src="../../assets/images/0028-1.jpg" />
			<p class="img" style="font-size: 14px">图1-9</p>
			</div>
			<p>我们来研究本节“观察思考”中的问题 (1).</p>
			<p>
			到2022年年底举办过夏季奥运会的城市组成集合A，举办过冬季奥运会的城市组成集合B，同时举办过两种奥运会的城市也组成一个集合C，这个集合中的元素既是集合A中的元素，又是集合B中的元素.也就是说，集合C是集合A与集合B的所有公共元素组成的集合，如图1-9所示.
			</p>
			<div class="img-rights openImgBox">
			<img class="img-c" alt="" src="../../assets/images/0028-2.jpg" />
			<p class="img" style="font-size: 14px">图1-10</p>
			</div>
			<p>
			再如，集合M={1，2}，集合P={1，2，3}，集合Q={1，2，5，6}，则集合M中的元素既是集合P中的元素，又是集合Q中的元素.集合M是集合P和集合Q中的所有公共元素组成的集合，如图1-10所示.
			</p>

			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>

			<div class="img-rights openImgBox">
			<img class="img-c" alt="" src="../../assets/images/0028-3.jpg" />
			<p class="img" style="font-size: 14px">图1-11</p>
			</div>
			<p>
			一般地，设A，B是两个集合，由属于A且属于B的所有元素组成的集合C叫作集合A与集合B的交集，记作A∩B，读作“A交B”，即
			</p>
			<p>C=A∩B={x\|x∈A且x∈B}.</p>
			<p>图1-11中的涂色部分表示集合A与集合B的交集.</p>

			<ul>
			<li>
			<div>
			<span class="zt-ls2">例1</span>设集合A={2，3，5，7}，B={-2，0，3，5，8}，求A∩B.
			</div>

			<span class="btn-box" @click="
			chapter001.isShowExample23 = !chapter001.isShowExample23
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample23">
			<p><span class="zt-ls2">解</span> A∩B={3，5}.</p>
			</li>
			<li>
			<div>
			<span class="zt-ls2">例2</span>设集合A={x\|-1＜x＜7}，B={x\|-3＜x≤3}，求A∩B.
			</div>

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			chapter001.isShowExample24 = !chapter001.isShowExample24
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			transform="translate(-3327.144 15329)" />
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			transform="translate(-3761 14334.001)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample24">
			<p>
			<span class="zt-ls2">解</span>在数轴上将集合A与B表示出来（如图1-12所示）.
			</p>
			</li>
			</ul>

			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/gn.jpg" />
			</p>
			</div>
			<p class="block">交集</p>
			</div>

			<p>观察可知 A∩B={x\|-1＜x≤3}.</p>
			<div class="center openImgBox">
			<img class="img-f" alt="" src="../../assets/images/0028-4.jpg" />
			<p class="img" style="font-size: 14px">图1-12</p>
			</div>
			</div>
			</div>
			</div>
			<!-- 018 -->
			<div class="page-box" page="25">
			<div v-if="showPageList.indexOf(25) > -1">
			<ul class="page-header-odd fl al-end">
			<li>018</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116">
			<ul>
			<li>
			<span class="zt-ls2">例3</span>设集合A={x\|x≤2}，B={x\|x＜-1}，求A∩B.

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			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample25">
			<p>
			<span class="zt-ls2">解</span>在数轴上将集合A，B表示出来（如图1-13所示）.
			</p>
			</li>
			</ul>
			<div class="center openImgBox">
			<img class="img-f" alt="" src="../../assets/images/0029-1.jpg" />
			<p class="img" style="font-size: 14px">图1-13</p>
			</div>
			<p>观察可知A∩B={x\|x＜-1}.</p>
			<ul>
			<li>
			<span class="zt-ls2">例4</span>设集合A={（x，y）\|x+2y-6=0}，B={（x，y）\|x-4y=0}，求A∩B.
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			transform="translate(-3327.144 15329)" />
			</svg>
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			transform="translate(-3761 14334.001)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample26">
			<div>
			<p>
			<span class="zt-ls"><b>解</b></span> 解方程组<math display="0">
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">{</mo>
			<mtable columnspacing="1em" rowspacing="4pt">
			<mtr>
			<mtd>
			<mi>x</mi>
			<mo>+</mo>
			<mn>2</mn>
			<mi>y</mi>
			<mo>−</mo>
			<mn>6</mn>
			<mo>=</mo>
			<mn>0</mn>
			</mtd>
			<mtd></mtd>
			</mtr>
			<mtr>
			<mtd>
			<mi>x</mi>
			<mo>−</mo>
			<mn>4</mn>
			<mi>y</mi>
			<mo>=</mo>
			<mn>0</mn>
			<mo>，</mo>
			</mtd>
			<mtd></mtd>
			</mtr>
			</mtable>
			<mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
			</mrow>
			</math>，得<math display="0">
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">{</mo>
			<mtable columnspacing="1em" rowspacing="4pt">
			<mtr>
			<mtd>
			<mi>x</mi>
			<mo>=</mo>
			<mn>4</mn>
			<mo>，</mo>
			</mtd>
			<mtd></mtd>
			</mtr>
			<mtr>
			<mtd>
			<mi>y</mi>
			<mo>=</mo>
			<mn>1.</mn>
			</mtd>
			<mtd></mtd>
			</mtr>
			</mtable>
			<mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
			</mrow>
			</math>.
			</p>
			<p>所以A∩B={（4，1）}.</p>
			</div>
			</li>
			</ul>
			<div class="textIndentation">
			根据交集的含义可以知道，对于任意两个集合A，B，有下述性质.
			<p>（1） A∩B=B∩A；（2） A∩A=A，A∩∅=∅；</p>
			<p>（3） A∩B⊆A，A∩B⊆B；（4）若A⊆B，则A∩B=A.</p>
			</div>
			<div class="bk-hzjl">
			<div class="bj1-hzjl">
			<p class="left">
			<img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
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			<examinations :cardList="questionData[25] ? questionData[25][1] : []" :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[25] ? questionData[25][2] : []" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
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			<!-- 019 -->
			<div class="page-box" page="26">
			<div v-if="showPageList.indexOf(26) > -1">
			<ul class="page-header-box">
			<li>
			<p>第一单元集合</p>
			</li>
			<li>
			<p><span>019</span></p>
			</li>
			</ul>
			<div class="padding-116">
			<h3>1.3.2 并集<span class="fontsz2">＞＞＞</span></h3>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>
			<div class="img-rights openImgBox">
			<img class="img-c" alt="" src="../../assets/images/0030-1.jpg" />
			<p class="img" style="font-size: 14px">图1-14</p>
			</div>
			<p>我们再来研究本节“观察思考”中的问题（2）.</p>
			<p>
			显然，我们只要把到2022年年底举办过夏季奥运会的城市或者举办过冬季奥运会的城市全部合并在一起就行了，这样合并在一起的城市就组成了一个新的集合，这个集合中的元素属于A或者属于B，如图1-14所示.
			</p>
			<div class="img-rights openImgBox">
			<img class="img-c" alt="" src="../../assets/images/0030-2.jpg" />
			<p class="img" style="font-size: 14px">图1-15</p>
			</div>
			<p>
			再如，集合P={a，b，c}，集合Q={a，b，d，e}，集合M={a，b，c，d，e}，集合M中的元素是由集合P或集合Q中的元素组成的（如图1-15所示）.
			</p>
			<div class="bk">
			<div class="bj1">
			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/gn.jpg" />
			</p>
			</div>
			<p class="block">并集</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>
			一般地，设A，B是两个集合，由所有属于A或者属于B的元素组成的集合C叫作集合A与集合B的并集，记作A∪B，读作“A并B”，即
			</p>
			<p>C=A∪B={x\|x∈A或x∈B}.</p>
			<p>图1-16（1）（2）中的涂色部分就表示集合A与集合B的并集.</p>
			<div class="center openImgBox">
			<img class="img-b" alt="" src="../../assets/images/0030-3.jpg" />
			<p class="img" style="font-size: 14px">图1-16</p>
			</div>
			=
			</div>
			</div>
			</div>
			<!-- 020 -->
			<div class="page-box" page="27">
			<div v-if="showPageList.indexOf(27) > -1">
			<ul class="page-header-odd fl al-end">
			<li>020</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116">
			<ul>
			<li>
			<span class="zt-ls2">例1</span>已知集合A={1，3，5，7，9}，B={2，3，5，7}，求A∪B.
			<span class="btn-box" @click="
			chapter001.isShowExample27 = !chapter001.isShowExample27
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample27">
			<p><span class="zt-ls2">解 </span>A∪B={1，2，3，5，7，9}.</p>
			</li>
			<li>
			<span class="zt-ls2">例2</span>已知集合A={x\|-1＜x＜7}，B={x\|-3＜x≤3}，求A∪B.

			<span class="btn-box" @click="
			chapter001.isShowExample28 = !chapter001.isShowExample28
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample28">
			<p>
			<span class="zt-ls2">解 </span>在数轴上将集合A，B表示出来（如图1-17所示）.
			</p>
			</li>
			</ul>
			<div class="center openImgBox">
			<img class="img-f" alt="" src="../../assets/images/0031-1.jpg" />
			<p class="img" style="font-size: 14px">图1-17</p>
			</div>
			<p>观察可知A∪B={x\|-3＜x＜7}.</p>
			<div class="bk-hzjl">
			<div class="bj1-hzjl">
			<p class="left">
			<img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
			</p>
			<examinations :cardList="questionData[27] ? questionData[27][1]:[] " :hideCollect="true" sourceType="json" v-if="questionData">
			</examinations>
			</div>
			</div>
			<ul>
			<li>
			<span class="zt-ls2">例3</span>设集合A={x\|x>4}, B={x\|x≤-2}, 求A∪B.
			<span class="btn-box" @click="
			chapter001.isShowExample29 = !chapter001.isShowExample29
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample29">
			<p>
			<span class="zt-ls2">解</span>在数轴上将集合A, B 表示出来,
			如图1-18所示.
			</p>
			</li>
			</ul>
			<div class="center openImgBox">
			<img class="img-f" alt="" src="../../assets/images/0031-2.jpg" />
			<p class="img" style="font-size: 14px">图1-18</p>
			</div>
			<p>观察可知A∪B={x\|x＞4或x≤-2}.</p>
			<p>根据并集的含义可以知道，对于任意两个集合A，B，有下述性质.</p>
			<p>（1） A∪B=B∪A；（2） A∪A=A，A∪∅=A；</p>
			<p>（3） A⊆A∪B，B⊆A∪B；（4）若B⊆A，则A∪B=A.</p>
			<div class="bk-hzjl">
			<div class="bj1-hzjl">
			<p class="left">
			<img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
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			<li>
			<p>第一单元集合</p>
			</li>
			<li>
			<p><span>021</span></p>
			</li>
			</ul>
			<div class="padding-116">
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
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			<h3>1.3.3 全集与补集<span class="fontsz2">＞＞＞</span></h3>

			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" />
			</p>

			<p>我们继续来研究本节“观察思考”中的问题（3） .</p>

			<div class="img-rights openImgBox">
			<img class="img-c" alt="" src="../../assets/images/0032-1.jpg" />
			<p class="img" style="font-size: 14px">图1-19</p>
			</div>

			<p>
			到2022年年底举办过夏季奥运会的城市组成的集合A是U的一个子集.在U中所有不属于A的元素就是到2022年年底没举办过夏季奥运会的城市，如图1-19所示.设这些城市组成的集合为P，则集合P也是U的一个子集.如果把U叫作全集，那么这时集合P叫作集合A在全集U中的补集，同样集合A也叫作集合P在全集U中的补集.
			</p>
			<p>
			再如，集合U={不大于10的正整数}，集合P={不大于10的正奇数}，集合Q={不大于10的正偶数}，显然，集合P是由集合U中不属于集合Q的元素组成的，所以，集合P是集合Q在全集U中的补集.同理，集合Q也是集合P在全集U中的补集.
			</p>
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			<ul class="page-header-odd fl al-end">
			<li>022</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116">
			<div class="bk">
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			<p class="left">
			<img class="img-gn1" alt="" src="../../assets/images/gn.jpg" />
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			<p class="block">全集</p>
			<p class="block">补集</p>
			</div>
			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" />
			</p>
			<p>
			一般地，如果一个集合含有我们研究的问题中涉及的全部元素，那么这个集合叫作全集，常用符号U表示.设U是全集，A是U的一个子集，则由U中所有不属于A的元素组成的集合叫作子集A在全集U中的补集（或余集），记作∁UA，读作“A在全集U中的补集”.即
			</p>
			<p>∁UA={x\|x∈U且x∉A}.</p>
			<div class="img-float openImgBox">
			<img class="img-c" alt="" src="../../assets/images/0033-1.jpg" />
			<p class="img" style="font-size: 14px">图1-20</p>
			</div>
			<p>图1-20中的涂色部分就表示∁UA.</p>
			<p>
			例如，全班同学组成的集合为U，全班女同学组成的集合为A，则全班男同学组成的集合B就是集合A在全集U中的补集.即
			</p>
			<p>B=∁UA={x\|x∈U且x∉A}.</p>
			<p>
			根据全集和补集的含义可以知道，对于全集U和它的一个子集A，有下述性质.
			</p>
			<p>（1） A∪（∁UA）=U；（2） A∩（∁UA）=∅；（3） ∁U（∁UA）=A.</p>
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			<p>
			<span class="zt-ls2">例1</span>设全集U={x\|x是小于10的自然数}，集合A={2，5，6，7}，B={1，3，5，7}.求：
			</p>
			<ul>
			<li>
			（1） A∩B和A∪B；
			<span class="btn-box" @click="
			chapter001.isShowExample30 = !chapter001.isShowExample30
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample30">
			<div>
			<p>
			<span class="zt-ls2">解</span>由U={0，1，2，3，4，5，6，7，8，9}，得
			</p>
			<p>（1） A∩B={5，7}，A∪B={1，2，3，5，6，7}.</p>
			</div>
			</li>
			<li>
			（2） ∁UA和∁UB；

			<span class="btn-box" @click="
			chapter001.isShowExample31 = !chapter001.isShowExample31
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample31">
			<div>
			<p>
			<span class="zt-ls2">解</span>由U={0，1，2，3，4，5，6，7，8，9}，得
			</p>
			<p>（2） ∁UA={0，1，3，4，8，9}，∁UB={0，2，4，6，8，9}.</p>
			</div>
			</li>
			<li>
			（3）（∁UA）∩（∁UB）；
			<span class="btn-box" @click="
			chapter001.isShowExample32 = !chapter001.isShowExample32
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample32">
			<div>
			<p>
			<span class="zt-ls2">解</span>由U={0，1，2，3，4，5，6，7，8，9}，得
			</p>
			<p>（3）（∁UA）∩（∁UB）={0，4，8，9}.</p>
			</div>
			</li>
			<li>
			（4） ∁U（A∪B）；
			<span class="btn-box" @click="
			chapter001.isShowExample33 = !chapter001.isShowExample33
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample33">
			<div>
			<p>
			<span class="zt-ls2">解</span>由U={0，1，2，3，4，5，6，7，8，9}，得
			</p>
			<p>（4） ∁U（A∪B）={0，4，8，9}.</p>
			</div>
			</li>
			<li>
			（5）（∁UA）∪（∁UB）；
			<span class="btn-box" @click="
			chapter001.isShowExample34 = !chapter001.isShowExample34
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
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			<li v-if="chapter001.isShowExample34">
			<div>
			<p>
			<span class="zt-ls2">解</span>由U={0，1，2，3，4，5，6，7，8，9}，得
			</p>
			<p>（5）（∁UA）∪（∁UB）={0，1，2，3，4，6，8，9}.</p>
			</div>
			</li>
			<li>
			（6） ∁U（A∩B）.
			<span class="btn-box" @click="
			chapter001.isShowExample35 = !chapter001.isShowExample35
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
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			<li v-if="chapter001.isShowExample35">
			<div>
			<p>
			<span class="zt-ls2">解</span>由U={0，1，2，3，4，5，6，7，8，9}，得
			</p>
			<p>（6） ∁U（A∩B）={0，1，2，3，4，6，8，9}.</p>
			</div>
			</li>
			</ul>
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			<!-- <drag :question="dragQuestion" :page="10"/> -->
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			<p>第一单元集合</p>
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			<li>
			<p><span>023</span></p>
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			</ul>
			<div class="padding-116">
			<p>
			<span class="zt-ls2">例2</span>设全集为R，集合A={x\|-2＜x＜5}，B={x\|-5＜x＜3}.求：
			</p>

			<ul>
			<li>
			（1）（A∩B）∪（A∪B）；
			<span class="btn-box" @click="
			chapter001.isShowExample36 = !chapter001.isShowExample36
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			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample36">
			<div>
			<p>
			<span class="zt-ls2">解 </span>在数轴上将集合A，B表示出来（如图1-21所示）.
			</p>
			<p>（1）观察图1-21，可得</p>
			<p>A∩B={x\|-2＜x＜3}，A∪B={x\|-5＜x＜5}，</p>
			<p>所以（A∩B）∪（A∪B）={x\|-5＜x＜5}.</p>
			</div>
			</li>
			<li>
			（2）（∁RA）∩（∁RB）；
			<span class="btn-box" @click="
			chapter001.isShowExample37 = !chapter001.isShowExample37
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample37">
			<div>
			<p>
			<span class="zt-ls2">解 </span>在数轴上将集合A，B表示出来（如图1-21所示）.
			</p>
			<p>（2） ∁RA={x\|x≤-2或x≥5}，∁RB={x\|x≤-5或x≥3}，</p>
			<p>所以（∁RA）∩（∁RB）={x\|x≤-5或x≥5}.</p>
			</div>
			</li>
			<li>
			（3）（∁RA）∩B；
			<span class="btn-box" @click="
			chapter001.isShowExample38 = !chapter001.isShowExample38
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample38">
			<div>
			<p>
			<span class="zt-ls2">解 </span>在数轴上将集合A，B表示出来（如图1-21所示）.
			</p>
			<p>（3）（∁RA）∩B={x\|-5＜x≤-2}.</p>
			</div>
			</li>
			<li>
			（4）（∁RB）∩A；
			<span class="btn-box" @click="
			chapter001.isShowExample39 = !chapter001.isShowExample39
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample39">
			<div>
			<p>
			<span class="zt-ls2">解 </span>在数轴上将集合A，B表示出来（如图1-21所示）.
			</p>
			<p>（4）（∁RB）∩A={x\|3≤x＜5}.</p>
			</div>
			</li>
			<li>
			（5）（∁RA）∪B；
			<span class="btn-box" @click="
			chapter001.isShowExample40 = !chapter001.isShowExample40
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample40">
			<div>
			<p>
			<span class="zt-ls2">解 </span>在数轴上将集合A，B表示出来（如图1-21所示）.
			</p>
			<p>（5）（∁RA）∪B={x\|x＜3或x≥5}.</p>
			</div>
			</li>
			<li>
			（6）（∁RB）∪A.
			<span class="btn-box" @click="
			chapter001.isShowExample41 = !chapter001.isShowExample41
			">
			<svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
			<path class="a"
			d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
			transform="translate(-3327.144 15329)" />
			</svg>
			</span>
			</li>
			<li v-if="chapter001.isShowExample41">
			<div>
			<p>
			<span class="zt-ls2">解 </span>在数轴上将集合A，B表示出来（如图1-21所示）.
			</p>
			<p>（6）（∁RB）∪A={x\|x≤-5或x＞-2}.</p>
			</div>
			</li>
			</ul>

			<div class="center openImgBox">
			<img class="img-d" alt="" src="../../assets/images/0034-1.jpg" />
			<p class="img" style="font-size: 14px">图1-21</p>
			</div>

			<div class="img-rights openImgBox">
			<img class="img-c" alt="" src="../../assets/images/0034-2.jpg" />
			<p class="img" style="font-size: 14px">图1-22</p>
			</div>

			<p>
			结合本节的例题，本节开始部分“观察思考”中问题（4）
			的答案也尽在其中了.
			</p>
			<p>
			如图1-22涂色部分所示，∁U（A∪B）表示到2022年年底既没举办过夏季奥运会也没举办过冬季奥运会的城市.
			</p>
			<p>
			求集合的交集、并集、补集是集合的三种运算.这里集合运算的含义如下：由两个已知的集合，按照某种指定的法则，得到一个新的集合.
			</p>

			<p class="left">
			<img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
			</p>
			<div class="bj">
			<examinations :cardList="questionData[30]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			</div>
			</div>
			</div>
			<!-- 024 -->
			<div class="page-box" page="31">
			<div v-if="showPageList.indexOf(31) > -1">
			<ul class="page-header-odd fl al-end">
			<li>024-025</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116">
			<h2 id="c031">习题1.3<span class="fontsz2"> ＞＞＞</span></h2>
			<div class="bj">
			<examinations :cardList="questionData[31]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			</div>
			</div>
			</div>
			<!-- 025 -->
			<div class="page-box hidePage" page="32">
			</div>
			<!-- 026 -->
			<div class="page-box" page="33">
			<div v-if="showPageList.indexOf(33) > -1">
			<ul class="page-header-odd fl al-end">
			<li>026</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116">
			<h2 id="c031">
			数学园地<span class="fontsz2">＞＞＞</span>
			<div style="font-size: 15px; margin-top: 5px">康托尔和集合论</div>
			</h2>

			<p>
			进入中职学校学习后，同学们会发现自己所学的第一个数学概念是：集合.研究集合的数学理论在现代数学中称为集合论.它是数学的一个基本分支，在数学中占据着重要的地位，其基本概念已渗透到数学的所有领域.如果把现代数学比作一座无比辉煌的大厦，那么可以说集合论正是构成这座大厦的基石.其创始人康托尔也因集合论的成就被誉为对20世纪数学发展影响最深的学者之一.
			</p>
			<p>
			康托尔（Georg
			Cantor，1845—1918），德国数学家，集合论的创始人.1845年3月3日生于圣彼得堡，1918年1月6日病逝于哈雷，其父是迁居俄国的丹麦商人.康托尔11岁时随家移居德国，自幼对数学有浓厚的兴趣.1862年，康托尔进入瑞士苏黎世大学，翌年转入柏林大学.1867年，康托尔获博士学位，之后他一直在哈雷大学任教，从事数学教学与研究.
			</p>
			<p>
			人们把康托尔于1873年12月7日最早提出集合论思想的那一天定为集合论诞生日.他对集合所下的定义如下：把若干确定的、有区别的（不论是具体的或抽象的）
			事物合并起来，看作一个整体，就称为一个集合，其中各事物称为该集合的元素.不到30岁的康托尔向神秘的“无穷”宣战，他靠着智慧和汗水，成功地证明了一条直线上的点能够和一个平面上的点一一对应，也能和空间中的点一一对应.这样看起来，1
			cm长的线段内的点与太平洋海面上的点以及整个地球内部的点都“一样多”.后来几年，康托尔对这类“无穷集合”问题发表了一系列文章，通过严格证明得出了许多惊人的结论.在中职数学中，我们所学习的只是集合论的最基本知识.学习过程中，同学们或许觉得一切都是很自然与简单的，根本无法想象它在诞生之日遭到激烈反对的情景，也体会不到康托尔的功绩之所在.
			</p>
			<p>
			事实证明，康托尔的集合论不仅为数学分析奠定了基础，而且对整个现代数学结构产生了重大而深远的影响.1897年举行的第一次国际数学家会议上，他的成就得到承认.
			</p>
			<p>
			如果你想知道康托尔和他的集合论在诞生之日不被理解、遭到激烈反对的情景，如果你想知道康托尔在当时受到的不公正待遇，如果你想知道康托尔坚持真理最后获得成功的过程，可以到网上搜索，你将会了解到更多关于康托尔和集合论的故事.
			</p>
			</div>
			</div>
			</div>
			<!-- 027 -->
			<div class="page-box" page="34">
			<div v-if="showPageList.indexOf(34) > -1">
			<ul class="page-header-box">
			<li>
			<p>第一单元集合</p>
			</li>
			<li>
			<p><span>027</span></p>
			</li>
			</ul>
			<div class="padding-116">
			<h2 id="c031" style="font-size: 25px">
			单元小结<span class="fontsz2">＞＞＞＞＞＞</span>
			</h2>
			<p class="bj2">
			<b>学习导图</b>
			</p>
			<div class="center openImgBox">
			<img class="img-b" alt="" src="../../assets/images/0038-1.jpg" />
			</div>
			<p class="bj2">
			<b>学习指导</b>
			</p>
			<div class="textIndentation">
			1.集合及其表示.
			<p>（1）由一些确定的对象所组成的整体就称为集合.</p>
			<p>（2）集合中元素的特征：①确定性；②互异性；③无序性.</p>
			<p>（3）符号“∈”和“∉”表示元素和集合之间的关系.</p>
			<p>
			（4）元素个数有限的集合，
			称为有限集；元素个数无限的集合，称为无限集.如果一个集合中没有任何元素，这样的集合叫作空集，
			记作 ∅.
			</p>
			<p>
			（5）常见数集的表示：自然数集N，正整数集N*
			或N+，整数集Z，有理数集Q，实数集R.
			</p>
			<p>
			（6）集合主要有两种表示方法：列举法和描述法.两种表示方法各有特点.
			</p>
			</div>
			<div class="textIndentation">
			2.集合之间的关系.
			<p>
			（1）对于两个集合A，B，
			若集合A中的任何一个元素都是集合B中的元素，则称集合A是集合B的子集，记作A⊆B（或B⊇A）；空集是任何集合的子集.
			</p>
			<p>
			（2）如果集合A是集合B的子集，且集合B中至少有一个元素不属于集合
			A，
			则集合A叫作集合B的真子集，记作A⫋B（或B⫌A）；空集是任何非空集合的真子集.
			</p>
			</div>
			</div>
			</div>
			</div>
			<!-- 028 -->
			<div class="page-box" page="35">
			<div v-if="showPageList.indexOf(35) > -1">
			<ul class="page-header-odd fl al-end">
			<li>028</li>
			<li>数学.基础模块</li>
			<li>上册</li>
			</ul>
			<div class="padding-116">
			<p>
			（3）对于两个集合A， B，如果A⊆B，且B⊆A，
			那么此时集合A与集合B的元素是完全一样的，称集合A与集合B相等.记作A=B.
			</p>
			<div class="textIndentation">
			3.集合的运算.
			<p>（1）两个集合的交集A∩B={x\|x∈A 且x∈B}.</p>
			<p>（2）两个集合的并集A∪B={x\|x∈A 或x∈B}.</p>
			<p>（3）集合的补集∁UA={x\|x∈U 且x∉A}.</p>
			</div>
			</div>
			</div>
			</div>
			<!-- 029-->
			<div class="page-box" page="36">
			<div v-if="showPageList.indexOf(36) > -1">
			<ul class="page-header-box">
			<li>
			<p>第一单元集合</p>
			</li>
			<li>
			<p><span>029-030</span></p>
			</li>
			</ul>
			<div class="padding-116">
			<h2 id="c031">单元检测<span class="fontsz2"> ＞＞＞＞＞＞</span></h2>
			<div class="bj">
			<examinations :cardList="questionData[36]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
			v-if="questionData"></examinations>
			</div>
			</div>
			</div>
			</div>
			<!-- 030 -->
			<div class="page-box hidePage" page="37">
			</div>

			<!-- 函数控件弹窗 -->
			<el-dialog
			:visible.sync="dialogVisible"
			width="60%"
			:append-to-body="true"
			:show-close="false"
			>
			<div slot="title" style="padding: 0 0 15px 0;position: relative;">
			<svg
			style="position: absolute; right:10px;cursor: pointer;"
			@click="dialogVisible = false"
			t="1718596022986"
			class="icon"
			viewBox="0 0 1024 1024"
			version="1.1"
			xmlns="http://www.w3.org/2000/svg"
			p-id="4252"
			width="20"
			height="20"
			xmlns:xlink="http://www.w3.org/1999/xlink"
			>
			<el-dialog :visible.sync="dialogVisible" width="60%" :append-to-body="true" :show-close="false">
			<div slot="title" style="padding: 0 0 15px 0; position: relative">
			<svg style="position: absolute; right: 10px; cursor: pointer" @click="dialogVisible = false" t="1718596022986"
			class="icon" viewBox="0 0 1024 1024" version="1.1" xmlns="http://www.w3.org/2000/svg" p-id="4252" width="20"
			height="20" xmlns:xlink="http://www.w3.org/1999/xlink">
			<path
			d="M176.661601 817.172881C168.472798 825.644055 168.701706 839.149636 177.172881 847.338438 185.644056 855.527241 199.149636 855.298332 207.338438 846.827157L826.005105 206.827157C834.193907 198.355983 833.964998 184.850403 825.493824 176.661601 817.02265 168.472798 803.517069 168.701706 795.328267 177.172881L176.661601 817.172881Z"
			fill="#979797"
			p-id="4253"
			></path>
			fill="#979797" p-id="4253"></path>
			<path
			d="M795.328267 846.827157C803.517069 855.298332 817.02265 855.527241 825.493824 847.338438 833.964998 839.149636 834.193907 825.644055 826.005105 817.172881L207.338438 177.172881C199.149636 168.701706 185.644056 168.472798 177.172881 176.661601 168.701706 184.850403 168.472798 198.355983 176.661601 206.827157L795.328267 846.827157Z"
			fill="#979797"
			p-id="4254"
			></path>
			fill="#979797" p-id="4254"></path>
			</svg>
			</div>
			<iframe
			src="https://www.geogebra.org/calculator"
			frameborder="0"
			style="width: 100%; min-height: 800px"
			></iframe>
			<iframe src="https://www.geogebra.org/calculator" frameborder="0" style="width: 100%; min-height: 800px"></iframe>
			</el-dialog>

			<!-- 解题思路弹窗 -->
			<el-dialog
			:visible.sync="thinkingDialog"
			width="40%"
			:append-to-body="true"
			:show-close="false"
			>
			<div slot="title" style="padding: 0; text-align: center; color: #333;display:flex;justify-content: center;">
			<span style=""> 解题思路 </span>
			<svg
			style="position: absolute; right:10px;cursor: pointer;"
			@click="thinkingDialog = false"
			t="1718596022986"
			class="icon"
			viewBox="0 0 1024 1024"
			version="1.1"
			xmlns="http://www.w3.org/2000/svg"
			p-id="4252"
			width="20"
			height="20"
			xmlns:xlink="http://www.w3.org/1999/xlink"
			>
			<el-dialog :visible.sync="thinkingDialog" width="40%" :append-to-body="true" :show-close="false" @close="closeDialog" class="thinkDialog" >
			<div slot="title" class="think-header" style="padding: 0; text-align: center; color: #333;display:flex;justify-content: center;">
			<span style=""> 分析 </span>
			<svg style="position: absolute; right:10px;cursor: pointer;" @click="thinkingDialog = false" t="1718596022986"
			class="icon" viewBox="0 0 1024 1024" version="1.1" xmlns="http://www.w3.org/2000/svg" p-id="4252" width="20"
			height="20" xmlns:xlink="http://www.w3.org/1999/xlink">
			<path
			d="M176.661601 817.172881C168.472798 825.644055 168.701706 839.149636 177.172881 847.338438 185.644056 855.527241 199.149636 855.298332 207.338438 846.827157L826.005105 206.827157C834.193907 198.355983 833.964998 184.850403 825.493824 176.661601 817.02265 168.472798 803.517069 168.701706 795.328267 177.172881L176.661601 817.172881Z"
			fill="#979797"
			p-id="4253"
			></path>
			fill="#979797" p-id="4253"></path>
			<path
			d="M795.328267 846.827157C803.517069 855.298332 817.02265 855.527241 825.493824 847.338438 833.964998 839.149636 834.193907 825.644055 826.005105 817.172881L207.338438 177.172881C199.149636 168.701706 185.644056 168.472798 177.172881 176.661601 168.701706 184.850403 168.472798 198.355983 176.661601 206.827157L795.328267 846.827157Z"
			fill="#979797"
			p-id="4254"
			></path>
			fill="#979797" p-id="4254"></path>
			</svg>
			</div>
			<ul>
			<li v-for="(item, index) in thinkOne" :key="index">
			<div v-if="item.isShow" style="display: flex">
			<li v-for="(item, index) in thinkData" :key="index">
			<div v-if="index <= showIndex" style="display: flex">
			<span style="position: relative">
			<span
			style="position: absolute; top: 16px; left: 13px; color: #fff"
			>{{ index + 1 }}</span
			>
			<img
			src="../../assets/images/icon/blue-group.png"
			alt=""
			style="margin-right: 10px"
			v-if="index < thinkOne.length - 1"
			/>
			<img
			src="../../assets/images/icon/blue.png"
			alt=""
			v-if="index == thinkOne.length - 1"
			style="margin-right: 10px"
			/>
			<span style="position: absolute; top: 4px; left: 13px; color: #fff">{{ index + 1 }}</span>
			<img src="../../assets/images/icon/blue-group.png" alt="" style="margin-right: 10px"
			v-if="index < thinkOne.length - 1" />
			<img src="../../assets/images/icon/blue.png" alt="" v-if="index == thinkOne.length - 1"
			style="margin-right: 10px" />
			</span>
			<p class="txt-p">{{ item.txt }}</p>
			<p class="txt-p" v-html="item"></p>
			</div>
			</li>
			</ul>
			<div
			@click="showNext(thinkIndex)"
			style="
			<div @click="changeNext" style="
			display: flex;
			flex-direction: column;
			align-items: center;
			justify-content: center;
			"
			>
			<img
			src="../../assets/images/icon/mouse.png"
			alt=""
			v-if="thinkIndex != 3"
			/>
			<svg
			xmlns="http://www.w3.org/2000/svg"
			xmlns:xlink="http://www.w3.org/1999/xlink"
			t="1710234570135"
			class="icon"
			viewBox="0 0 1024 1024"
			version="1.1"
			p-id="5067"
			width="15"
			height="15"
			>
			">
			<img src="../../assets/images/icon/mouse.png" alt="" v-if="showIndex < thinkData.length - 1" />
			<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" t="1710234570135"
			class="icon" viewBox="0 0 1024 1024" version="1.1" p-id="5067" width="15" height="15">
			<path
			d="M2.257993 493.371555 415.470783 906.584344 512 1003.113561 608.529217 906.584344 1021.742007 493.371555 925.212789 396.842337 512 810.055127 98.787211 396.842337Z"
			fill="#1296db"
			p-id="5068"
			/>
			fill="#1296db" p-id="5068" />
			<path
			d="M2.257993 117.980154 415.470783 531.192944 512 627.722161 608.529217 531.192944 1021.742007 117.980154 925.212789 21.450937 512 434.663727 98.787211 21.450937Z"
			fill="#1296db"
			p-id="5069"
			/>
			</svg>
			</div>
			</el-dialog>
			<!-- 解题步骤弹窗 -->
			<el-dialog
			class="stepDialog"
			title="解题步骤"
			:visible.sync="stepDialog"
			width="40%"
			:append-to-body="true"
			:show-close="false"
			>
			<div slot="title" style="padding: 0; text-align: center; color: #333;display:flex;justify-content: center;">
			<span>
			解题步骤
			</span>
			<svg
			style="position: absolute; right:10px;cursor: pointer;"
			@click="stepDialog = false"
			t="1718596022986"
			class="icon"
			viewBox="0 0 1024 1024"
			version="1.1"
			xmlns="http://www.w3.org/2000/svg"
			p-id="4252"
			width="20"
			height="20"
			xmlns:xlink="http://www.w3.org/1999/xlink"
			>
			<path
			d="M176.661601 817.172881C168.472798 825.644055 168.701706 839.149636 177.172881 847.338438 185.644056 855.527241 199.149636 855.298332 207.338438 846.827157L826.005105 206.827157C834.193907 198.355983 833.964998 184.850403 825.493824 176.661601 817.02265 168.472798 803.517069 168.701706 795.328267 177.172881L176.661601 817.172881Z"
			fill="#979797"
			p-id="4253"
			></path>
			<path
			d="M795.328267 846.827157C803.517069 855.298332 817.02265 855.527241 825.493824 847.338438 833.964998 839.149636 834.193907 825.644055 826.005105 817.172881L207.338438 177.172881C199.149636 168.701706 185.644056 168.472798 177.172881 176.661601 168.701706 184.850403 168.472798 198.355983 176.661601 206.827157L795.328267 846.827157Z"
			fill="#979797"
			p-id="4254"
			></path>
			</svg>
			</div>
			<ul>
			<li v-for="(item, index) in stepOne" :key="index">
			<div v-if="item.isShow" style="display: flex">
			<span style="position: relative">
			<span
			style="position: absolute; top: 16px; left: 13px; color: #fff"
			>{{ index + 1 }}</span
			>
			<img
			src="../../assets/images/icon/blue-group.png"
			alt=""
			style="margin-right: 10px"
			v-if="index < stepOne.length - 1"
			/>
			<img
			src="../../assets/images/icon/blue.png"
			alt=""
			v-if="index == stepOne.length - 1"
			style="margin-right: 10px"
			/>
			</span>
			<p class="txt-p">{{ item.txt }}</p>
			</div>
			</li>
			</ul>
			<div
			@click="showNextChange(stepIndex)"
			style="
			display: flex;
			flex-direction: column;
			align-items: center;
			justify-content: center;
			"
			>
			<img
			src="../../assets/images/icon/mouse.png"
			alt=""
			v-if="stepIndex != 2"
			/>
			<svg
			xmlns="http://www.w3.org/2000/svg"
			xmlns:xlink="http://www.w3.org/1999/xlink"
			t="1710234570135"
			class="icon"
			viewBox="0 0 1024 1024"
			version="1.1"
			p-id="5067"
			width="15"
			height="15"
			>
			<path
			d="M2.257993 493.371555 415.470783 906.584344 512 1003.113561 608.529217 906.584344 1021.742007 493.371555 925.212789 396.842337 512 810.055127 98.787211 396.842337Z"
			fill="#1296db"
			p-id="5068"
			/>
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			d="M2.257993 117.980154 415.470783 531.192944 512 627.722161 608.529217 531.192944 1021.742007 117.980154 925.212789 21.450937 512 434.663727 98.787211 21.450937Z"
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			</svg>
			</div>
			</el-dialog>
			@@ -820,235 +2170,185 @@
			</template>

			<script>
			import examinations from "@/components/examinations/index.vue";
			import { getResourcePath } from "@/assets/methods/resources";
			import { getCollectResource,setCollectResource } from "@/assets/methods/resources";
			import drag from '@/components/dragQuestion/index.vue'
			import graffiti from "@/components/graffiti/index.vue"
			import examinations from '@/components/examinations/index.vue'
			import { getResourcePath } from '@/assets/methods/resources'
			import {
			getCollectResource,
			setCollectResource,
			} from '@/assets/methods/resources'
			export default {
			name: "chapter-one",
			components: { examinations,drag,graffiti },
			name: 'chapter-one',
			components: { examinations },
			props: {
			showPageList: {
			type: Array,
			default: [],
			},
			questionData:{
			type:Object
			}
			questionData: {
			type: Object,
			},
			},
			async mounted() {
			const data = localStorage.getItem("math-chapterData");
			const data = localStorage.getItem('math-chapterData')
			if (data) {
			this.chapterData = JSON.parse(data);
			this.chapterData = JSON.parse(data)
			}
			this.getPath();
			this.collectResourceList = await getCollectResource(this.config.activeBook.bookId)
			this.getPath()
			this.collectResourceList = await getCollectResource(
			this.config.activeBook.bookId
			)
			},
			data() {
			return {
			collectImg: require("../../assets/images/icon/heart.png"),
			collectCheck: require("../../assets/images/icon/heart-check.png"),
			isShowExampleOne: false,
			isShowExampleTwo: false,
			isShowExampleThree: false,
			isShowExampleFour: false,
			isShowExampleFive: false,
			chapter001: {
			tkItem01: {
			text1: '',
			},
			isShowExample1: false,
			isShowExample2: false,
			isShowExample3: false,
			isShowExample4: false,
			isShowExample5: false,
			isShowExample6: false,
			isShowExample7: false,
			isShowExample8: false,
			isShowExample9: false,
			isShowExample10: false,
			isShowExample11: false,
			isShowExample12: false,
			isShowExample13: false,
			isShowExample14: false,
			isShowExample15: false,
			isShowExample16: false,
			isShowExample17: false,
			isShowExample18: false,
			isShowExample19: false,
			isShowExample20: false,
			isShowExample21: false,
			isShowExample22: false,
			isShowExample23: false,
			isShowExample24: false,
			isShowExample25: false,
			isShowExample26: false,
			isShowExample27: false,
			isShowExample28: false,
			isShowExample29: false,
			isShowExample30: false,
			isShowExample31: false,
			isShowExample32: false,
			isShowExample33: false,
			isShowExample34: false,
			isShowExample35: false,
			isShowExample36: false,
			isShowExample37: false,
			isShowExample38: false,
			isShowExample39: false,
			isShowExample40: false,
			isShowExample41: false,
			},
			collectImg: require('../../assets/images/icon/heart.png'),
			collectCheck: require('../../assets/images/icon/heart-check.png'),
			dialogVisible: false,
			thinkingDialog: false,
			stepDialog: false,
			videoPath: "",
			videoPath: '',
			stepIndex: 1,
			thinkIndex: 1,
			collectResourceList:[],
			collectResourceList: [],
			chapterData: {
			isCollectImg: false,
			isCollectVideo: false,
			txtOne: "",
			txtTwo: "",
			txtOne: '',
			txtTwo: '',
			},
			thinkOne: [
			{
			txt: "1:一个函数是不是偶函数,可以由函数的图像是否关于y 轴对称来判断;当函数用解析法表示时,可以用偶函数的定义来判断。偶函数:一般地，设函数f(x)的定义域为D，如果对于任意xED，都有XED，且f(-x)=f(x)，那么函数f(x)就叫作偶函数",
			isShow: true,
			},
			{
			txt: "2:计算f(-x)",
			isShow: false,
			},
			{
			txt: "3:判断f(-x)是否等于f(x)",
			isShow: false,
			},
			],
			stepOne: [
			{
			txt: "1:(1)函数f(x)=3x2+1的定义域是R，对任意XER，都有-XER",
			txt: '1:(1)函数f(x)=3x2+1的定义域是R，对任意XER，都有-XER',
			isShow: true,
			},
			{
			txt: "2:f(-x)=3(-x)2+1=3x2+1=f(x)",
			txt: '2:f(-x)=3(-x)2+1=3x2+1=f(x)',
			isShow: false,
			},
			],
			dragQuestion:[
			{
			analysisCon: null,
			answer: ['A','B','C'],
			difficulty: 0,
			id: "7BC7B760",
			isCollect: false,
			isComplete: false,
			isRight: null,
			isUnfold: "",
			isUserAnswer: false,
			number: 1,
			option: [
			{
			img: "",
			index: "010311",
			txt: "胆小的",
			value: "A",
			isShow:true
			},
			{
			img: "",
			index: "010312",
			txt: "善良的",
			value: "B",
			isShow:true
			},
			{
			img: "",
			index: "010313",
			txt: "沉稳的",
			value: "C",
			isShow:true
			},
			],
			optionStyle: "Txt",
			questionType: "drag",
			score: 2,
			stem: {
			0: "蚂蚁队长走路昂首挺胸、步伐坚定，它是一只(",
			1:{
			data: "span",
			num: 0
			},
			2: ")蚂蚁;小蚂蚁走起路来小心翼翼，眼神飘忽不定，它是一只(",
			3:{
			data:"span",
			num:1
			},
			4:")蚂蚁;蚂蚁小妹面带微笑，时刻愿意帮助大家，它是一只(",
			5:{
			data:"span",
			num:2,
			},
			6:" )蚂蚁"
			},
			stemStyle: "RichTxt",
			type: "拖拽题",
			userAnswer:[
			{
			vlaue:'',
			txt:''
			},
			{
			vlaue:'',
			txt:''
			},
			{
			vlaue:'',
			txt:''
			},
			]
			},
			]
			};
			// 新增
			thinkData:[],
			thinkOne: [
			'分析为了不重不漏地写出集合A 的所有子集,我们应分为以下几个步骤来写.',
			'（1） ∅是所有集合的子集，所以先写出 ∅；',
			'（2）写出含有一个元素的子集：{a}，{b}，{c}；',
			'（3）写出含有两个元素的子集：{a，b}，{a，c}，{b，c}；',
			'（4）写出含有三个元素的子集：{a，b，c}'
			],
			thinkTwo:[
			"（1）因为“英文大写”这一条件是明确的，所以“英文大写字母”是确定的对象.",
			"（2）因为“高个子”这一条件不明确，所以它所指的对象不确定.",
			"（3）解不等式2x-7＜0得 x ＜ 7 2 .任意一个实数，都可以和 7 2比较大小，所以不等式2x-7＜0的所有实数解都是确定的对象.",
			"（4）任意一个正整数，能否被5整除是确定的，所以能被5整除的正整数能组成集合."
			],
			thinkThree:['用描述法表示集合，关键是找出集合中元素所具有的共同特征.根据对共同特征的描述必须能判定任一对象是否属于这个集合.'],
			thinkFour:['可先将已知集合在数轴上表示出来，然后观察得出交集，但是一定要注意分析端点的情况.'],
			thinkFive:[`集合A表示方程x+2y-6=0的解集，集合B表示方程x-4y=0
			的解集，两个解集的交集就是二元一次方程组

			<math display="block">
			<mrow data-mjx-texclass="INNER">
			<mo data-mjx-texclass="OPEN">{</mo>
			<mtable columnalign="left" columnspacing="1em" rowspacing="4pt">
			<mtr>
			<mtd>
			<mi>x</mi>
			<mo>+</mo>
			<mn>2</mn>
			<mi>y</mi>
			<mo>−</mo>
			<mn>6</mn>
			<mo>=</mo>
			<mn>0</mn>
			<mo>,</mo>
			</mtd>
			</mtr>
			<mtr>
			<mtd>
			<mi>x</mi>
			<mo>−</mo>
			<mn>4</mn>
			<mi>y</mi>
			<mo>=</mo>
			<mn>0</mn>
			</mtd>
			</mtr>
			</mtable>
			<mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
			</mrow>
			</math>

			<p>的解集.</p> `],
			showIndex:0,
			}
			},
			created() {
			const localData = JSON.parse(localStorage.getItem('chapter001'))
			if (localData) {
			this.chapter001 = { ...Object.assign(this.chapter001, localData) }
			}
			},
			methods: {
			handleChapterData() {
			localStorage.setItem(
			"math-chapterData",
			JSON.stringify(this.chapterData)
			);
			},
			async getPath() {
			this.videoPath = await getResourcePath(
			"a28cd862d61b5df2201406b76e9f01b0"
			);
			},
			// getQuestionData() {
			// axios
			// .get(this.config.activeBook.resourceUrl + "/question.json")
			// .then((res) => {
			// let oldAnswer = localStorage.getItem(
			// this.config.activeBook.name + "oldAnswerData"
			// );
			// if (oldAnswer) {
			// oldAnswer = JSON.parse(oldAnswer);
			// console.log("旧数据", oldAnswer);
			// if (oldAnswer[9]) {
			// for (let index = 0; index < res.data.data.length; index++) {
			// const item = res.data.data[index];
			// if (item.infoList.length) {
			// for (
			// let cindex = 0;
			// cindex < item.infoList.length;
			// cindex++
			// ) {
			// const citem = item.infoList[cindex];
			// const question = oldAnswer[9].find(
			// (ditem) => ditem.id == citem.id
			// );
			// if (question) {
			// citem.userAnswer = question.userAnswer;
			// }
			// }
			// }
			// }
			// }
			// }
			// this.questionData = res.data.data;
			// });
			// },
			handleCollect(type) {
			if (type == "img") {
			this.handleCollectResource("722FE833","",'images/0101-1.jpg',"图片","json",'图3-15')
			} else if (type == "video") {
			this.handleCollectResource("a28cd862d61b5df2201406b76e9f01b0","a28cd862d61b5df2201406b76e9f01b0",'',"视频","bits",'视频：判数函数奇偶性的方法和步骤')
			// setCollectResource(this.config.activeBook.bookId,[])
			}
			this.handleChapterData();
			},
			openMathDiaolog() {
			this.dialogVisible = true;
			},
			openThinkingDialog() {
			this.thinkingDialog = true;
			},
			showNext(num) {
			const number = this.thinkOne.findIndex((item, index) => index == num);
			console.log(number);
			this.thinkOne[number].isShow = true;
			if (this.thinkIndex <= 2) {
			this.thinkIndex++;
			}
			},
			showNextChange(num) {
			const number = this.stepOne.findIndex((item, index) => index == num);
			this.stepOne[number].isShow = true;
			if (this.stepIndex < 2) {
			this.stepIndex++;
			}
			this.videoPath = await getResourcePath('a28cd862d61b5df2201406b76e9f01b0')
			console.log(this.videoPath, '0988')
			},
			//资源收藏事件
			handleCollectResource(id,md5,resourcePath,resourceType,source,resourceName){
			console.log(this.collectResourceList);
			handleCollectResource(
			id,
			md5,
			resourcePath,
			resourceType,
			source,
			resourceName
			) {
			console.log(this.collectResourceList)
			let list = this.collectResourceList
			if(list.findIndex(item => item.id == id) > -1) {
			list = list.filter(item => item.id != id)
			if (list.findIndex((item) => item.id == id) > -1) {
			list = list.filter((item) => item.id != id)
			} else {
			list.push({
			id,
			@@ -1060,10 +2360,24 @@
			})
			}
			this.collectResourceList = list
			setCollectResource(this.config.activeBook.bookId,this.collectResourceList)
			setCollectResource(
			this.config.activeBook.bookId,
			this.collectResourceList
			)
			},
			// 新增
			openDialog(queryData) {
			this.thinkData = queryData
			this.thinkingDialog = !this.thinkingDialog
			},
			closeDialog() {
			this.showIndex = 0
			},
			changeNext() {
			if(this.showIndex < this.thinkData.length - 1) this.showIndex = this.showIndex + 1
			}
			},
			};
			}
			</script>

			<style lang="less" scoped>
			@@ -1071,27 +2385,36 @@
			font-size: 18px;
			text-align: justify;
			}

			.iframe-box {
			width: 100%;
			min-height: 800px;
			border: 1px solid #00a1e9;
			border-radius: 10px;
			}

			li {
			list-style: none;
			display: flex;
			align-items: center;
			line-height: 50px;
			}

			.txt-p {
			margin-top: 0;
			padding: 10px 0;
			}

			.bottom-btn {
			display: flex;
			flex-direction: column;
			align-items: center;
			justify-content: center;
			}

			.step-num {
			position: relative;

			.step-num-box {
			position: absolute;
			top: 16px;
			@@ -1099,6 +2422,5 @@
			color: #fff;
			}
			}
			.stepDialog {
			}

			</style>