全集U={1,2,3,4,5,6,7,8},A={3,4,5},B={1,3,6},那么C={2,7,8}是( )
A.C∪B
B.A∩B
C.(C∪A)∩(C∪B)
D.(C∪A)∪(C∪B)
【答案】分析:由題設知CUB={2,4,5,7,8}≠C;A∩B={3}≠C;(C∪A)∩(C∪B)={2,3,4,5,7,8}∩{1,2,3,6,7,8}={2,7,8}=C;(C∪A)∪(C∪B)={2,3,4,5,7,8}∪{1,2,3,6,7,8,}={1,2,3,4,5,6,7,8}≠C.
解答:解:∵全集U={1,2,3,4,5,6,7,8},
A={3,4,5},B={1,3,6},C={2,7,8}
∴CUB={2,4,5,7,8}≠C,故A不正確;
A∩B={3}≠C,故B不正確;
(CUA)∩(CUB)={1,2,6,7,8}∩{2,4,5,7,8}={2,7,8}=C,故C正確;
(CUA)∪(CUB)={1,2,6,7,8}∪{2,4,5,7,8,}={1,2,4,5,6,7,8}≠C,故D不成立.
故選C.
點評:本題考查集合的交、并、補集的混合運算,是基礎題,解題時要認真審題,仔細解答,注意合理地進行等價轉(zhuǎn)化.