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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.证明如下蕴含式：<br>
(1)<img src="image/cunzai.gif" width="7" height="11">xA(x)<img src="image/yunhan.gif" width="15" height="9"><img src="image/renyi.gif" width="9" height="11">xB(x)<img src="image/tuichu.gif" width="15" height="9"><img src="image/renyi.gif" width="9" height="11">x(A(x)<img src="image/yunhan.gif" width="15" height="9">B(x))<br>
(2)<img src="image/renyi.gif" width="9" height="11">xA(x)<img src="image/xiqu.gif" width="9" height="15"><img src="image/renyi.gif" width="9" height="11">xB(x)<img src="image/tuichu.gif" width="15" height="9"><img src="image/renyi.gif" width="9" height="11">x(A(x)<img src="image/xiqu.gif" width="9" height="15">B(x))<br>
(3)<img src="image/cunzai.gif" width="7" height="11">x(A(x)<img src="image/hequ.gif" width="9" height="11">B(x))<img src="image/tuichu.gif" width="15" height="9"><img src="image/cunzai.gif" width="7" height="11">xA(x)<img src="image/hequ.gif" width="9" height="11"><img src="image/cunzai.gif" width="7" height="11">xB(x)<br>
(4)P(x)<img src="image/hequ.gif" width="9" height="11"><img src="image/renyi.gif" width="9" height="11">xQ(x)<img src="image/tuichu.gif" width="15" height="9"><img src="image/cunzai.gif" width="7" height="11">x(P(x)<img src="image/hequ.gif" width="9" height="11">Q(x))
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<p style="line-height: 150%" >2.设个体域是非负整数集合 N={0,1,2,...}。试证明蕴含式 <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/hequ.gif" width="9" height="11">Q(y))<img src="image/tuichu.gif" width="15" height="9"><img src="image/cunzai.gif" width="7" height="11">xP(x)
成立。 </p>
<p style="line-height: 150%" >3.用构成推导过程的方法，证明下列蕴涵式：<br>
(1)<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">x((P(x)<img src="image/xiqu.gif" width="9" height="15">Q(x)<img src="image/yunhan.gif" width="15" height="9">R(x)),
<img src="image/cunzai.gif" width="7" height="11">xP(x),
<img src="image/cunzai.gif" width="7" height="11">xQ(x)<img src="image/tuichu.gif" width="15" height="9"><img src="image/cunzai.gif" width="7" height="11">x<img src="image/cunzai.gif" width="7" height="11">y(R(x)<img src="image/hequ.gif" width="9" height="11">R(y))<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/tuichu.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))</p>
<p style="line-height: 150%" >4.下列推导步骤中，哪些是错误的？<br>
(1) (a) <img src="image/renyi.gif" width="9" height="11">xP(x)<img src="image/yunhan.gif" width="15" height="9">Q(x)
<br>
(b) P(x)<img src="image/yunhan.gif" width="15" height="9">Q(x)<br>
(2) (a) <img src="image/renyi.gif" width="9" height="11">x(P(x)<img src="image/xiqu.gif" width="9" height="15">Q(x))<br>
(b) P(a)<img src="image/xiqu.gif" width="9" height="15">Q(b)<br>
(3) (a) P(x)<img src="image/yunhan.gif" width="15" height="9">Q(x)<br>
(b) <img src="image/cunzai.gif" width="7" height="11">xP(x)<img src="image/yunhan.gif" width="15" height="9">Q(x)<br>
(4) (a) P(a)<img src="image/yunhan.gif" width="15" height="9">P(b)<br>
(b) <img src="image/cunzai.gif" width="7" height="11">x(P(x)<img src="image/yunhan.gif" width="15" height="9">Q(x))<br>
5.试找出下列推导过程中的错误，并问问结论是否有效？如果是，写出真确的推导过程：<br>
{1} (1) <img src="image/renyi.gif" width="9" height="11">x(P(x)<img src="image/yunhan.gif" width="15" height="9">Q(x)) P<br>
{2} (2) P(y)<img src="image/yunhan.gif" width="15" height="9">Q(y)
US,(1)<br>
{3} (3) <img src="image/cunzai.gif" width="7" height="11">xP(x) P<br>
{3} (4) P(y) ES,(3)<br>
{1,3} (5) Q(y) T,(2),(4),I11<br>
{1,3} (6) <img src="image/cunzai.gif" width="7" height="11">xQ(x) EG,(5)</p>
<p style="line-height: 150%" ></p>
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