content-4-1-1.htm

实用的离散数学课件

          <p style="line-height: 150%">&nbsp; x(R<img border="0" src="Image/bing.gif" width="14" height="14">S)y<img border="0" src="Image/dengjia.gif" width="17" height="9">(xRy)<img border="0" src="Image/xiqu.gif" width="9" height="15">(xSy)</p>         
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        <li>         
          <p style="line-height: 150%">&nbsp; x(R<img border="0" src="Image/jiao.gif" width="14" height="15">S)y<img border="0" src="Image/dengjia.gif" width="17" height="9">(xRy)<img src="image/hequ.gif" width="9" height="11">(xSy)</p>         
        </li>         
        <li>         
          <p style="line-height: 150%">&nbsp; x(R-S)y<img border="0" src="Image/dengjia.gif" width="17" height="9">(xRy)<img src="image/hequ.gif" width="9" height="11"><img border="0" src="Image/fei.gif" width="10" height="5">(xSy)</p>         
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          <p style="line-height: 150%">&nbsp; x(~R)y<img border="0" src="Image/dengjia.gif" width="17" height="9"><img border="0" src="Image/fei.gif" width="10" height="5">(xRy)</p>         
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      <p style="line-height: 150%">　</p>   
      <p style="line-height: 150%"><b>7、二元关系的表示</b></p>   
      <p style="line-height: 150%"><b>&nbsp; </b>关系是一种集合，因而集合的表示方法均可用于表示关系(如谓词逻辑)，此外，还可以用关系矩阵和关系图来描述一个关系。</p>   
      <p style="line-height: 150%">&nbsp;&nbsp;&nbsp; <b>a)关系矩阵</b></p>         
      <p style="line-height: 150%">&nbsp; 设集合A={a1,a2,…,an},B={b1,b2,…,bn},R时一个从A到B的二元关系,如果矩阵<img src="Image/mr.gif" width="22" height="15" >=[<img src="Image/rij1.gif" width="12" height="13">]中     
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            <td width="16%" rowspan="2"><img src="Image/rij1.gif" width="12" height="13">=</td>     
            <td width="84%">0，&nbsp;&nbsp; 若 <img border="0" src="Image/fei.gif" width="10" height="5">(ai      
              R bj)</td>     
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          <tr>     
            <td width="84%">1，&nbsp;&nbsp; 若 (ai R bj)</td>     
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        </center>     
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      <p style="line-height: 150%">则称<img src="Image/mr.gif" width="22" height="15">为R的关系矩阵。     
      </p>      
      <p style="line-height: 150%">&nbsp; <b>例：</b>设A={1,2,3,4},B={1,2,3},A到B的二元关系R={&lt;x,y&gt;|x&gt;y},求<img src="Image/mr.gif" width="22" height="15" >。     
      </p>      
      <p style="line-height: 150%">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; R={&lt;x,y&gt;|x&gt;y}={&lt;4,1&gt;,&lt;4,2&gt;,&lt;4,3&gt;,&lt;3,1&gt;,&lt;3,2&gt;,&lt;2,1&gt;}&nbsp;     
      </p>      
      <div align="center">     
        <center>     
        <table border="0" width="34%" cellpadding="0" cellspacing="1">     
          <tr>     
            <td width="25%" rowspan="4">     
              <p align="center"><img src="Image/mr.gif" width="22" height="15">=</td>     
            <td width="25%" style="border-left-style: solid" align="center">0</td>     
            <td width="25%" align="center">0</td>     
            <td width="25%" style="border-right-style: solid" align="center">0</td>     
          </tr>     
          <tr>     
            <td width="25%" style="border-left-style: solid" align="center">1</td>     
            <td width="25%" align="center">0</td>     
            <td width="25%" style="border-right-style: solid" align="center">0</td>     
          </tr>     
          <tr>     
            <td width="25%" style="border-left-style: solid" align="center">1</td>     
            <td width="25%" align="center">1</td>     
            <td width="25%" style="border-right-style: solid" align="center">0</td>     
          </tr>     
          <tr>     
            <td width="25%" style="border-left-style: solid" align="center">1</td>     
            <td width="25%" align="center">1</td>     
            <td width="25%" style="border-right-style: solid" align="center">1</td>     
          </tr>     
        </table>     
        </center>     
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      <p style="line-height: 150%">　   
      </p>    
      <p style="line-height: 150%">&nbsp;&nbsp;&nbsp; <b>b)关系图</b>     
      </p>      
      <p style="line-height: 150%">&nbsp; 设R是A上的二元关系，则R的关系图可表示为G(A,R)，G中的点与集合A中的元素相对应，如果有&lt;<img src="Image/xi.gif" width="10" height="11">,<img border="0" src="Image/xj.gif" width="13" height="13">&gt;<img border="0" src="image/shuyu.gif" width="13" height="11">R      
      (<img border="0" src="Image/xi.gif" width="10" height="11">,<img border="0" src="Image/xj.gif" width="13" height="13"><img border="0" src="image/shuyu.gif" width="13" height="11">A)，则从<img src="Image/xi.gif" width="10" height="11">到<img border="0" src="Image/xj.gif" width="13" height="13">用带箭头的直线或者弧线画一条线，若有&lt;<img src="Image/xi.gif" width="10" height="11">,<img src="Image/xi.gif" width="10" height="11">&gt;<img border="0" src="image/shuyu.gif" width="13" height="11">R，则在<img src="Image/xi.gif" width="10" height="11">处画一条自封闭的直线。   
      </p>    
      <p style="line-height: 150%">&nbsp; <b>例：</b>设A={1,2,3,4}，R={&lt;4,1&gt;,&lt;1,2&gt;,&lt;2,2&gt;,&lt;3,3&gt;}，则该关系的关系图为：   
      </p>    
      <p style="line-height: 150%" align="center"><img border="0" src="Image/gxt1.gif" width="154" height="126">   
      </p>    
      <p style="line-height: 150%" align="center">　   
      </p>    
      <p style="line-height: 150%" align="left">&nbsp;&nbsp;&nbsp;    
      通常，两个集合之间元素的二元关系用关系矩阵来表示，一个集合内部元素的二元关系用关系图直接给出。   
      </p>    
      <p style="line-height: 150%" align="center">　   
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      <p style="line-height: 150%" align="center">　   
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      <p style="line-height: 150%" align="center">&nbsp;&nbsp;   
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