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</span></span></td>
</tr>
<tr>
<td width="25%" align="center"><img border="0" src="image/fei.gif" width="10" height="5">P<img border="0" src="image/hequ.gif" width="9" height="11">
Q<img border="0" src="image/hequ.gif" width="9" height="11"> R</td>
<td width="25%" align="center">011</td>
<td width="25%" align="center">3</td>
<td width="25%" align="center"><span style="mso-text-raise: -6.0pt; 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" lang="EN-US"><img src="Image/m3.gif" v:shapes="_x0000_i1027" width="16" height="11"></span></td>
</tr>
<tr>
<td width="25%" align="center"> P<img border="0" src="image/hequ.gif" width="9" height="11"><img border="0" src="image/fei.gif" width="10" height="5">Q<img border="0" src="image/hequ.gif" width="9" height="11"><img border="0" src="image/fei.gif" width="10" height="5">R</td>
<td width="25%" align="center">100</td>
<td width="25%" align="center">4</td>
<td width="25%" align="center"><span style="mso-text-raise: -5.0pt; 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" lang="EN-US"><img src="Image/m4.gif" v:shapes="_x0000_i1028" width="16" height="11"></span></td>
</tr>
<tr>
<td width="25%" align="center"> P<img border="0" src="image/hequ.gif" width="9" height="11"><img border="0" src="image/fei.gif" width="10" height="5">Q<img border="0" src="image/hequ.gif" width="9" height="11">
R</td>
<td width="25%" align="center">101</td>
<td width="25%" align="center">5</td>
<td width="25%" align="center"><span style="mso-text-raise: -6.0pt; 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" lang="EN-US"><img src="Image/m5.gif" v:shapes="_x0000_i1029" width="16" height="11"></span></td>
</tr>
<tr>
<td width="25%" align="center"> P<img border="0" src="image/hequ.gif" width="9" height="11">
Q<img border="0" src="image/hequ.gif" width="9" height="11"><img border="0" src="image/fei.gif" width="10" height="5">R</td>
<td width="25%" align="center">110</td>
<td width="25%" align="center">6</td>
<td width="25%" align="center"><span style="mso-text-raise: -6.0pt; 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" lang="EN-US"><img src="Image/m6.gif" v:shapes="_x0000_i1030" width="16" height="11"></span></td>
</tr>
<tr>
<td width="25%" align="center"> P<img border="0" src="image/hequ.gif" width="9" height="11">
Q<img border="0" src="image/hequ.gif" width="9" height="11"> R</td>
<td width="25%" align="center">111</td>
<td width="25%" align="center">7</td>
<td width="25%" align="center"><span style="mso-text-raise: -6.0pt; 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" lang="EN-US"><img src="Image/m7.gif" v:shapes="_x0000_i1031" width="16" height="11"></span></td>
</tr>
</table>
</center>
</div>
<p style="line-height: 150%"><b><br>
2、主析取范式 ：</b>对于给定的命题公式，仅含有极小项的析取的等价公式，称为该给定公式的主析取范式。
</p>
<blockquote>
<p style="line-height: 150%"><b>性质1</b> ： 对于任何已知的命题公式
A(P1,P2,...,Pn),P1,P2,...,Pn 是其中的 n 个命题变元，则一定能够直接构成与其等价的主析取范式。<br>
</p>
<p style="line-height: 150%"><b>性质2</b> ： 永真式无主析取范式。
</p>
</blockquote>
<p style="line-height: 150%"><b>求范式的基本步骤 ：</b>
</p>
<ol>
<li>
<p style="line-height: 150%" align="left">消去联结词<img border="0" src="image/yunhan.gif" width="15" height="9">、<img src="image/dengtong.gif" width="16" height="9">；</li>
<li>
<p style="line-height: 150%" align="left">将否定联结词深入到原子命题前面；</li>
<li>
<p style="line-height: 150%" align="left">利用分配律化为析取范式或合取范式；</li>
<li>
<p style="line-height: 150%" align="left">再添加变元构成主析取范式，主合取范式。</li>
</ol>
<p style="line-height: 150%">例：求下列公式的主析取范式
</p>
<blockquote>
<ol>
<li>
<p style="line-height: 150%">P<img border="0" src="image/yunhan.gif" width="15" height="9">Q</li>
<li>
<p style="line-height: 150%">P<img src="image/dengtong.gif" width="16" height="9">Q</li>
<li>
<p style="line-height: 150%"><img border="0" src="image/fei.gif" width="10" height="5">P<img border="0" src="image/xiqu.gif" width="9" height="15">Q</li>
<li>
<p style="line-height: 150%">P<img border="0" src="image/yunhan.gif" width="15" height="9">((P<img border="0" src="image/yunhan.gif" width="15" height="9">Q)<img border="0" src="image/hequ.gif" width="9" height="11"><img border="0" src="image/fei.gif" width="10" height="5">(<img border="0" src="image/fei.gif" width="10" height="5">Q<img border="0" src="image/xiqu.gif" width="9" height="15"><img border="0" src="image/fei.gif" width="10" height="5">P)</li>
</ol>
<p style="line-height: 150%"> <p style="line-height: 150%">
</blockquote>
<p style="line-height: 150%"> <b><font color="#FF0000">注：</font>主析取范式与真值表之间的关系</b>
</p>
<p style="line-height: 150%">
若将极小项的二进制编码与他的一组指派相对应，如<img border="0" src="image/fei.gif" width="10" height="5">P<img border="0" src="image/hequ.gif" width="9" height="11">
Q<img border="0" src="image/hequ.gif" width="9" height="11"><img border="0" src="image/fei.gif" width="10" height="5">R与0、1、0，则当且仅当用这组指派代入该极小项时极小项为真。<br>
由此可知，在命题公式的<b>主析取范式中每个极小项与真值表中的成真指派一一对应。</b>一个命题公式的真值表是唯一的，所以公式的主析取范式也是唯一的。<br>
要判断两个公式是否等价的另一种方式:<b>判断两个公式的主析取范式是否相等.</b>
</p>
<p style="line-height: 150%"><b> <font color="#FF0000">*</font>主析取范式的个数</b>
</p>
<p style="line-height: 150%"><b> </b>一般来说,由n个变元构成的公式由无限多个,但是每个公式都有一个唯一的主析取范式,如果两个公式由相同的主析取范式我们说这两个公式是等价的.那么,由n个变元构成的公式由多少种不同的主析取范式呢?这是可以计算出来的:
</p>
<p style="line-height: 150%"> n=1时,有2个极小项,可以构成4个主析取范式;<br>
n=2时,有4个极小项,可以构成16个主析取范式;<br>
以此类推,n个变元,有<img border="0" src="Image/2den.gif" width="13" height="12">个极小项,可以构成<span lang="EN-US" style="font-size:10.5pt;mso-bidi-font-size:
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<img src="Image/2de2den.gif" v:shapes="_x0000_i1025" width="17" height="14"></span></span>个主析取范式.<span lang="EN-US" style="font-size:10.5pt;mso-bidi-font-size:
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</p>
<p style="line-height: 150%" align="left"><b>3、极大项 ：</b>在有 n 个命题变元的基本和中，若每个变元与其否定并不同时存在，且二者之一必出现一次且仅出现一次，则这种基本和称为极大项。
</p>
<p style="line-height: 150%" align="center">如：P<img border="0" src="image/xiqu.gif" width="9" height="15">Q<img border="0" src="image/xiqu.gif" width="9" height="15">R、<img border="0" src="image/fei.gif" width="10" height="5">P<img border="0" src="image/xiqu.gif" width="9" height="15"><img border="0" src="image/fei.gif" width="10" height="5">Q<img border="0" src="image/xiqu.gif" width="9" height="15">R
</p>
<p style="line-height: 150%" align="left">则n个变元可以构成<img border="0" src="Image/2den.gif" width="13" height="12">个不同的极小项。如，3个变元P、Q、R可以构成8个极小项。
</p>
<p style="line-height: 150%" align="left">
我们把命题变元看成“0”，而命题变元的否定看成“1”，那么，若把P、Q、R按照一定的顺序排列下来可以把每个极小项依次对应于一个三位二进制数。如下：
</p>
<div align="center">
<center>
<table border="1" width="60%">
<tr>
<td width="25%" align="center">
<p align="center">极大项</td>
<td width="25%" align="center">二进制编码</td>
<td width="25%" align="center">对应的数</td>
<td width="25%" align="center">记作</td>
</tr>
<tr>
<td width="25%" align="center"> P<img border="0" src="image/xiqu.gif" width="9" height="15">
Q<img border="0" src="image/xiqu.gif" width="9" height="15"> R</td>
<td width="25%" align="center">000</td>
<td width="25%" align="center">0</td>
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