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</td>
<td width="25%" align="center">
<p style="line-height: 200%">有</p>
</td>
<td width="25%" align="center">
<p style="line-height: 200%">有</p>
</td>
</tr>
<tr>
<td width="25%" align="center">
<p style="line-height: 200%">5</p>
</td>
<td width="25%" align="center">
<p style="line-height: 200%">无</p>
</td>
<td width="25%" align="center">
<p style="line-height: 200%">有</p>
</td>
<td width="25%" align="center">
<p style="line-height: 200%">无</p>
</td>
</tr>
<tr>
<td width="25%" align="center">
<p style="line-height: 200%">6</p>
</td>
<td width="25%" align="center">
<p style="line-height: 200%">无</p>
</td>
<td width="25%" align="center">
<p style="line-height: 200%">有</p>
</td>
<td width="25%" align="center">
<p style="line-height: 200%">有</p>
</td>
</tr>
</table>
</center>
</div>
<p style="line-height: 200%"> 求,上述三中设备至少有一种的计算机的台数.</p>
<p style="line-height: 200%"> 解:设用<img src="image/a1.gif" width="12" height="15" >
、<img src="image/a2.gif" width="14" height="15">、
<img src="image/a3.gif" width="14" height="15">分别表示具有三中设备的计算机的集合</p>
<p style="line-height: 200%"> 则|<img src="image/a1.gif" width="12" height="15" >|=2、|<img src="image/a2.gif" width="14" height="15">|=5、|<img src="image/a3.gif" width="14" height="15">|=3，</p>
<p style="line-height: 200%"> |<img src="image/a1.gif" width="12" height="15" ><img border="0" src="image/jiao.gif" width="14" height="15"><img src="image/a2.gif" width="14" height="15">|=2、|<img src="image/a2.gif" width="14" height="15"><img border="0" src="image/jiao.gif" width="14" height="15"><img src="image/a3.gif" width="14" height="15">|=3、|<img src="image/a1.gif" width="12" height="15" ><img border="0" src="image/jiao.gif" width="14" height="15"><img src="image/a3.gif" width="14" height="15">|=1</p>
<p style="line-height: 200%"> |<img src="image/a1.gif" width="12" height="15" ><img border="0" src="image/jiao.gif" width="14" height="15"><img src="image/a2.gif" width="14" height="15"><img border="0" src="image/jiao.gif" width="14" height="15"><img src="image/a3.gif" width="14" height="15">|=1</p>
<p style="line-height: 200%"> 所以 |<img src="image/a1.gif" width="12" height="15" >
<img border="0" src="image/bing.gif" width="14" height="14"><img src="image/a2.gif" width="14" height="15"><img border="0" src="image/bing.gif" width="14" height="14">
<img src="image/a3.gif" width="14" height="15">|
</p>
<p style="line-height: 200%">
= |<img src="image/a1.gif" width="12" height="15" >|+|<img src="image/a2.gif" width="14" height="15">|+|<img src="image/a3.gif" width="14" height="15">|-|<img src="image/a1.gif" width="12" height="15" ><img border="0" src="image/jiao.gif" width="14" height="15"><img src="image/a2.gif" width="14" height="15">|-|<img src="image/a2.gif" width="14" height="15"><img border="0" src="image/jiao.gif" width="14" height="15"><img src="image/a3.gif" width="14" height="15">|-|<img src="image/a1.gif" width="12" height="15" ><img border="0" src="image/jiao.gif" width="14" height="15"><img src="image/a3.gif" width="14" height="15">|+|<img src="image/a1.gif" width="12" height="15" ><img border="0" src="image/jiao.gif" width="14" height="15"><img src="image/a2.gif" width="14" height="15"><img border="0" src="image/jiao.gif" width="14" height="15"><img src="image/a3.gif" width="14" height="15">|</p>
<p style="line-height: 200%"> =2+5+3-2-1-3+1=5(台)</p>
<p style="line-height: 200%"> </p>
<p style="line-height: 200%"><b>推广(包含排斥原理)</b>:</p>
<p style="line-height: 200%" align="left"> |<img src="image/a1.gif" width="12" height="15" ><img border="0" src="image/bing.gif" width="14" height="14"><img src="image/a2.gif" width="14" height="15"><img border="0" src="image/bing.gif" width="14" height="14"><img src="image/a3.gif" width="14" height="15"><img border="0" src="image/bing.gif" width="14" height="14">…<img border="0" src="image/bing.gif" width="14" height="14"><img src="image/an.gif" width="14" height="15">|
= </p>
<p style="line-height: 200%" align="center">
<i>
<img src="image/conten11.gif" width="371" height="60"> <br>
<img src="image/conten12.gif" width="180" height="54"></i></p>
<p style="line-height: 200%">
公式的证明可以由数学归纳法来证明（略）</p>
<p style="line-height: 200%">
根据对偶原理可得出对偶公式：</p>
<p style="line-height: 200%">|<img src="image/a1.gif" width="12" height="15" ><img border="0" src="image/jiao.gif" width="14" height="15"><img src="image/a2.gif" width="14" height="15"><img border="0" src="image/jiao.gif" width="14" height="15"><img src="image/a3.gif" width="14" height="15"><img border="0" src="image/jiao.gif" width="14" height="15">…<img border="0" src="image/jiao.gif" width="14" height="15"><img src="image/an.gif" width="14" height="15">|
=</p>
<p style="line-height: 200%" align="center"><i><img src="image/conten13.gif" width="371" height="60"><br>
<img src="image/conten14.gif" width="173" height="54">
</i></p>
<p style="line-height: 200%"><b>
例：</b></p>
<ol dynamicoutline initcollapsed>
<li>
<p style="line-height: 200%">某单位装配了30辆汽车,其中15辆有录音机,8辆有空调,6辆有座位调节,三种设备都有的有3辆,问这三种设备都没有的至少有几辆?</p>
<ul dynamicoutline msimagelist imagesrc="Image/gif/nothing.gif">
<li>
<p style="line-height: 200%">解:设<img src="image/a1.gif" width="12" height="15" >={x|x装有录音机}、<img src="image/a2.gif" width="14" height="15">={x|x装有空调}、<img src="image/a3.gif" width="14" height="15">={x|x装有座位调节}<br>
则 |<img src="image/a1.gif" width="12" height="15" >|=15、|<img src="image/a2.gif" width="14" height="15">|=8、|<img src="image/a3.gif" width="14" height="15">|=6，|<img src="image/a1.gif" width="12" height="15" ><img border="0" src="image/jiao.gif" width="14" height="15"><img src="image/a2.gif" width="14" height="15"><img border="0" src="image/jiao.gif" width="14" height="15"><img src="image/a3.gif" width="14" height="15">|=3</p>
</li>
</ul>
<p style="line-height: 200%"> </p>
</li>
<li>
<p style="line-height: 200%">确定在不大于50的自然数中，能被2、3、5、7中任一个数整除的数的个数。</p>
</li>
</ol>
<p style="line-height: 200%"> </p>
<p style="line-height: 200%"> </p>
<p style="line-height: 200%" align="center"></p>
<p style="line-height: 200%" align="center"><i><a href="#作业" target="_self">作业</a></i></p>
<p style="line-height: 200%"> </p>
<p style="line-height: 200%"> </p>
<p style="line-height: 200%"> </p>
<p style="line-height: 200%"> </p>
<p style="line-height: 200%"> </p>
<p style="line-height: 200%"> </p>
<p style="line-height: 200%"><a name="作业">作业</a></p>
<p style="line-height: 200%">
某院学生选课情况如下，260人选艺术课，208人选生物课，160人选计算机课，76人选艺术与生物，48人选计算机与艺术，62人选生物和计算机，30人全选，150人都不选，求：（1）共有多少人？（2）有多少人选生物但不选计算机或生物？</p>
<p style="line-height: 200%"> </p>
</td>
</tr>
</table>
<table width="100%" border="0" cellspacing="0" cellpadding="0">
<tr>
<td>
<div align="center">
<p style="line-height: 200%"> <img src="IMAGE/yuancheng_2.gif" width="100" height="69"></div>
</td>
</tr>
</table>
<p style="line-height: 200%"> </p>
<p style="line-height: 150%"> </p><p align="right"><b><a href="contentFrame-mulu.htm"><<back</a></b>
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