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<p style="line-height: 150%" align="center"><font size="2">本 節 習 題</font> </p>
<p style="line-height: 150%" >1.設 E={a,b,c,d,e},A={a,d},B={a,b,e} 和 C={b,d}.試求出下列的集合：<br>
(1)A<img src="image/jiao.gif" width="10" height="14">~B<br>
(2)(A<img src="image/jiao.gif" width="10" height="14">B)<img src="image/bing.gif" width="10" height="14">~C<br>
(3)~(A<img src="image/jiao.gif" width="10" height="14">B)<br>
(4)~A<img src="image/bing.gif" width="10" height="14">~B
</p>
<p style="line-height: 150%" >2.給定自然數集合 N 的下列子集：<br>
A={1,2,7,8}<br>
B={i|i*i<50}<br>
C={i|i 可被 3 整除且 0 <img src="image/xiaodeng.GIF" width="9" height="10" >i <img src="image/xiaodeng.GIF" width="9" height="10" >30}<br>
D={i|i=2k,k<img src="image/shuyu.gif" width="13" height="11">I,0<k<6}<br>
試求出下列集合：<br>
(1)A<img src="image/bing.gif" width="10" height="14">(B<img src="image/bing.gif" width="10" height="14">(C<img src="image/bing.gif" width="10" height="14">D))<br>
(2)A<img src="image/jiao.gif" width="10" height="14">(B<img src="image/jiao.gif" width="10" height="14">(C<img src="image/jiao.gif" width="10" height="14">D))<br>
(3)B-(A<img src="image/bing.gif" width="10" height="14">C)<br>
(4)(~A<img src="image/jiao.gif" width="10" height="14">B)<img src="image/bing.gif" width="10" height="14">D</p>
<p style="line-height: 150%" >3.給定正整數集合 I+ 的下列子集：<br>
A={n|n<12}<br>
B={n|n <img src="image/xiaodeng.GIF" width="9" height="10" >8}<br>
C={n|n=2k,k<img src="image/shuyu.gif" width="13" height="11">I+}<br>
D={n|n=3k,k<img src="image/shuyu.gif" width="13" height="11">I+}<br>
F={n|n=2k-1,k<img src="image/shuyu.gif" width="13" height="11">I+}<br>
試用集合 A,B,C,D 和 F 表達下列集合：<br>
(1){2,4,6,8}<br>
(2){3,6,9}<br>
(3){10}<br>
(4){n|n 是偶數，n>10}<br>
(5){n|n 是正偶數且 n <img src="image/xiaodeng.GIF" width="9" height="10" >10，或n
是正奇數且 n >= 9}</p>
<p style="line-height: 150%" >4.設集合 A={2,3,4},B={1,2}，C={4,5,6}，試求出 A+B,B+C,A+B+C
和 (A+B)+(B+C)。</p>
<p style="line-height: 150%" >5.設 A,B 和 C 是全集 E 的子集，下列關系是否成立？<br>
(A<img src="image/bing.gif" width="10" height="14">B)<img src="image/jiao.gif" width="10" height="14">~(B<img src="image/bing.gif" width="10" height="14">C)<img src="image/baohan.gif" width="11" height="10">A<img src="image/jiao.gif" width="10" height="14">~B
</p>
<p style="line-height: 150%" >6.設 A,B 是全集 E 的子集，證明下列恒等式：<br>
(1)(A<img src="image/jiao.gif" width="10" height="14">B)<img src="image/bing.gif" width="10" height="14">(A<img src="image/jiao.gif" width="10" height="14">~B)=A<br>
(2)(B<img src="image/bing.gif" width="10" height="14">~((~A<img src="image/bing.gif" width="10" height="14">B)<img src="image/jiao.gif" width="10" height="14">A)=E<br>
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