📄 content-4-2-1.htm
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<p align="center">
M<sub>R</sub>=M<sub>R1<img border="0" src="Image/juhao.gif" width="8" height="13">R2</sub>=M<sub>R1</sub>·M<sub>R2</sub>
<p> 其中矩阵的乘法为<b>逻辑乘法</b>:</p>
<p style="line-height: 150%" align="left" > 即,在矩阵的乘法过程中加法换成逻辑加法,乘法换成逻辑乘法。 </p>
<p style="line-height: 150%" align="center" ><b>逻辑加法</b>：1+1=1+0=0+1=1、0+0=0 </p>
<p style="line-height: 150%" align="center" ><b>逻辑乘法</b>：1*1=1、1*0=0*1=0*0=0 </p>
<p style="line-height: 150%" align="left" > </p>
<p style="line-height: 150%" align="left" ><b>性质:</b> </p>
<ul>
<li>
<p style="line-height: 150%" align="left">关系合成不具有交换律.</li>
<li>
<p style="line-height: 150%" align="left">若R为A上的二元关系,I<sub>A</sub>为A上的恒等关系,则有R<img border="0" src="Image/juhao.gif" width="8" height="13">I<sub>A</sub>=I<sub>A</sub><img border="0" src="Image/juhao.gif" width="8" height="13">R=R.</li>
<li>
<p style="line-height: 150%" align="left">若R为A上的二元关系,<img border="0" src="Image/kong.gif" width="11" height="11">为A上的空关系,则有R<img border="0" src="Image/juhao.gif" width="8" height="13"><img border="0" src="Image/kong.gif" width="11" height="11">=<img border="0" src="Image/kong.gif" width="11" height="11"><img border="0" src="Image/juhao.gif" width="8" height="13">R=R.</li>
</ul>
<p style="line-height: 150%" align="left" ><b>定理1:</b> </p>
<p style="line-height: 150%" align="left" ><b> </b> 给定集合
X,Y,Z 和 W。设 <img src="image/R1.gif" width="13" height="15">
是从 X 到 Y 的<a href="content-4-1-1.htm#content-4-1-1-guanxi">关系</a>；<img src="image/R2.gif" width="14" height="15">
和 <img src="image/R3.gif" width="14" height="15">
都是从 Y 到 Z 的关系，<img src="image/R41.gif" width="15" height="14">
是从 Z 到 W 的关系,于是应有： </p>
<blockquote>
<p style="line-height: 150%" align="left" >
(1)<img src="image/R1.gif" width="13" height="15"><img src="image/juhao.GIF" width="8" height="13">(<img src="image/R2.gif" width="14" height="15"><img src="image/bing.gif" width="14" height="14"><img src="image/R3.gif" width="14" height="15">)=<img src="image/R1.gif" width="13" height="15"><img src="image/juhao.GIF" width="8" height="13"><img src="image/R2.gif" width="14" height="15"><img src="image/bing.gif" width="14" height="14"><img src="image/R1.gif" width="13" height="15"><img src="image/juhao.GIF" width="8" height="13"><img src="image/R3.gif" width="14" height="15"><br>
(2) <img src="image/R1.gif" width="13" height="15"><img src="image/juhao.GIF" width="8" height="13">(<img src="image/R2.gif" width="14" height="15"><img src="image/jiao.gif" width="14" height="15"><img src="image/R3.gif" width="14" height="15">)<img src="image/baohan.gif" width="11" height="10"><img src="image/R1.gif" width="13" height="15"><img src="image/juhao.GIF" width="8" height="13"><img src="image/R2.gif" width="14" height="15"><img src="image/jiao.gif" width="14" height="15"><img src="image/R1.gif" width="13" height="15"><img src="image/juhao.GIF" width="8" height="13"><img src="image/R3.gif" width="14" height="15"><br>
(3)(<img src="image/R2.gif" width="14" height="15"><img src="image/bing.gif" width="14" height="14"><img src="image/R3.gif" width="14" height="15">)<img src="image/juhao.GIF" width="8" height="13"><img src="image/R41.gif" width="15" height="14">=<img src="image/R2.gif" width="14" height="15"><img src="image/juhao.GIF" width="8" height="13"><img src="image/R41.gif" width="15" height="14"><img src="image/bing.gif" width="14" height="14"><img src="image/R3.gif" width="14" height="15"><img src="image/juhao.GIF" width="8" height="13"><img src="image/R41.gif" width="15" height="14"><br>
(4)(<img src="image/R2.gif" width="14" height="15"><img src="image/jiao.gif" width="14" height="15"><img src="image/R3.gif" width="14" height="15">)<img src="image/juhao.GIF" width="8" height="13"><img src="image/R41.gif" width="15" height="14"><img src="image/baohan.gif" width="11" height="10"><img src="image/R2.gif" width="14" height="15"><img src="image/juhao.GIF" width="8" height="13"><img src="image/R41.gif" width="15" height="14"><img src="image/jiao.gif" width="14" height="15"><img src="image/R3.gif" width="14" height="15"><img src="image/juhao.GIF" width="8" height="13"><img src="image/R41.gif" width="15" height="14"><span lang="EN-US" style="font-size:10.5pt;mso-bidi-font-size:
12.0pt;font-family:"Times New Roman";mso-fareast-font-family:宋体;mso-font-kerning:
1.0pt;mso-ansi-language:EN-US;mso-fareast-language:ZH-CN;mso-bidi-language:
AR-SA"><span style="mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shapetype
id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
<v:stroke joinstyle="miter"/>
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0"/>
<v:f eqn="sum @0 1 0"/>
<v:f eqn="sum 0 0 @1"/>
<v:f eqn="prod @2 1 2"/>
<v:f eqn="prod @3 21600 pixelWidth"/>
<v:f eqn="prod @3 21600 pixelHeight"/>
<v:f eqn="sum @0 0 1"/>
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</span>
</span> </p>
</blockquote>
<p style="line-height: 150%" align="left"><b>证明(1)(略)</b><span lang="EN-US" style="font-size:10.5pt;mso-bidi-font-size:
12.0pt;font-family:"Times New Roman";mso-fareast-font-family:宋体;mso-font-kerning:
1.0pt;mso-ansi-language:EN-US;mso-fareast-language:ZH-CN;mso-bidi-language:
AR-SA"><!--[if gte mso 9]><xml>
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DrawAspect="Content" ObjectID="_1080639375">
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</span> </p>
<p style="line-height: 150%" align="left" >
</p>
<p style="line-height: 150%" align="left" >
<b>
定理2:</b> </p>
<p style="line-height: 150%" align="left" >
设 X,Y,Z 和 W
都是集合,<img src="image/R1.gif" width="13" height="15">
是从 X 到 Y 的<a href="content-4-1-1.htm#content-4-1-1-guanxi">关系</a>；<img src="image/R2.gif" width="14" height="15">
是从 Y 到 Z 的关系；<img src="image/R3.gif" width="14" height="15">
是从 Z 到 W 的关系，于是有 (<img src="image/R1.gif" width="13" height="15"><img src="image/juhao.GIF" width="8" height="13"><img src="image/R2.gif" width="14" height="15">)<img src="image/juhao.GIF" width="8" height="13"><img src="image/R3.gif" width="14" height="15">=<img src="image/R1.gif" width="13" height="15"><img src="image/juhao.GIF" width="8" height="13">(<img src="image/R2.gif" width="14" height="15"><img src="image/juhao.GIF" width="8" height="13"><img src="image/R3.gif" width="14" height="15">)。 </p>
<p style="line-height: 150%" align="left" >
</p>
<p style="line-height: 150%" align="left" >
</p>
<p style="line-height: 150%" align="left" >
</p>
<p style="line-height: 150%" align="left" >
<b>关系合成的应用:</b> </p>
<p style="line-height: 150%" align="center" >
关系具有传递性<img border="0" src="Image/dengjia.gif" width="17" height="9">R<img src="image/juhao.GIF" width="8" height="13">R<img border="0" src="image/baohan.gif" width="11" height="10">R. </p>
<p style="line-height: 150%" align="left" >
</p>
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<p style="line-height: 150%" align="center"> </p>
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