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<p style="line-height: 150%" align="center"><font size="2">本 节 习 题</font> </p>
<p style="line-height: 150%" >1.证明如下等价式：<br>
(1)<img src="image/renyi.gif" width="9" height="11">xA(x)<img src="image/yunhan.gif" width="15" height="9">B<img src="image/dengjia.gif" width="17" height="9"><img src="image/cunzai.gif" width="7" height="11">x(A(x)<img src="image/yunhan.gif" width="15" height="9">B)<br>
(2)<img src="image/cunzai.gif" width="7" height="11">xA(x)<img src="image/yunhan.gif" width="15" height="9">B<img src="image/dengjia.gif" width="17" height="9"><img src="image/renyi.gif" width="9" height="11">x(A(x)<img src="image/yunhan.gif" width="15" height="9">B)<br>
(3)A<img src="image/yunhan.gif" width="15" height="9"><img src="image/renyi.gif" width="9" height="11">xB(x)<img src="image/dengjia.gif" width="17" height="9"><img src="image/renyi.gif" width="9" height="11">x(A<img src="image/yunhan.gif" width="15" height="9">B(x))<br>
(4)A<img src="image/yunhan.gif" width="15" height="9"><img src="image/cunzai.gif" width="7" height="11">xB(x)<img src="image/dengjia.gif" width="17" height="9"><img src="image/cunzai.gif" width="7" height="11">x(A<img src="image/yunhan.gif" width="15" height="9">B(x))</p>
<p style="line-height: 150%" >2.给出下列命题：<br>
(1)<img src="image/renyi.gif" width="9" height="11">x(P(x)<img src="image/yunhan.gif" width="15" height="9">Q(x))<img src="image/yunhan.gif" width="15" height="9">(<img src="image/renyi.gif" width="9" height="11">xP(x)<img src="image/yunhan.gif" width="15" height="9"><img src="image/renyi.gif" width="9" height="11">xQ(x))<br>
(2)(<img src="image/cunzai.gif" width="7" height="11">xP(x)<img src="image/yunhan.gif" width="15" height="9"><img src="image/renyi.gif" width="9" height="11">xQ(x))<img src="image/yunhan.gif" width="15" height="9"><img src="image/renyi.gif" width="9" height="11">x(P(x)<img src="image/yunhan.gif" width="15" height="9">Q(x))<br>
(3)<img src="image/renyi.gif" width="9" height="11">x(P(x)<img src="image/yunhan.gif" width="15" height="9">Q(x))<img src="image/yunhan.gif" width="15" height="9">(<img src="image/cunzai.gif" width="7" height="11">xP(x)<img src="image/yunhan.gif" width="15" height="9"><img src="image/renyi.gif" width="9" height="11">xQ(x))<br>
试判断哪个的真值是真的？试给出证明；若是假的，给出反例。</p>
<p style="line-height: 150%" >3.设个体域是非负整数集合 N={0,1,2,...}。试证明下列各式都能成立：<br>
(1)<img src="image/renyi.gif" width="9" height="11">x<img src="image/renyi.gif" width="9" height="11">y(P(x)<img src="image/xiqu.gif" width="9" height="15">Q(y))<img src="image/dengjia.gif" width="17" height="9"><img src="image/renyi.gif" width="9" height="11">xP(x)<img src="image/xiqu.gif" width="9" height="15"><img src="image/renyi.gif" width="9" height="11">yQ(y)<br>
(2)<img src="image/renyi.gif" width="9" height="11">x<img src="image/renyi.gif" width="9" height="11">y(P(x)<img src="image/hequ.gif" width="9" height="11">Q(y))<img src="image/dengjia.gif" width="17" height="9"><img src="image/renyi.gif" width="9" height="11">xP(x)<img src="image/hequ.gif" width="9" height="11"><img src="image/renyi.gif" width="9" height="11">yQ(y)<br>
(3)<img src="image/renyi.gif" width="9" height="11">x<img src="image/renyi.gif" width="9" height="11">y(P(x)<img src="image/yunhan.gif" width="15" height="9">Q(y))<img src="image/dengjia.gif" width="17" height="9"><img src="image/cunzai.gif" width="7" height="11">xP(x)<img src="image/yunhan.gif" width="15" height="9"><img src="image/renyi.gif" width="9" height="11">yQ(y)<br>
(4)<img src="image/cunzai.gif" width="7" height="11">x<img src="image/cunzai.gif" width="7" height="11">y(P(x)<img src="image/yunhan.gif" width="15" height="9">Q(y))<img src="image/dengjia.gif" width="17" height="9"><img src="image/renyi.gif" width="9" height="11">xP(x)<img src="image/yunhan.gif" width="15" height="9"><img src="image/cunzai.gif" width="7" height="11">yQ(y)</p>
<p style="line-height: 150%" >4.试证明 <img src="image/cunzai.gif" width="7" height="11">y<img src="image/renyi.gif" width="9" height="11">xP(x,y)
的否定等价于 <img src="image/renyi.gif" width="9" height="11">y<img src="image/cunzai.gif" width="7" height="11">x<img src="image/fei.gif" width="10" height="5">P(x,y)。</p>
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