设U={x∈Z|0<x≤10},A={1,2,4,5,9},B={4,6,7,8,10},C={3,5,7},求A∩B,A∪B,(CUA)∩(CUB),(CUA)∪(

发布时间:2020-07-31 19:51:18

设U={x∈Z|0<x≤10},A={1,2,4,5,9},B={4,6,7,8,10},C={3,5,7},求A∩B,A∪B,(CUA)∩(CUB),(CUA)∪(CUB),(A∩B)∩C,(A∪B)∩C.

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解:∵U={x∈Z|0<x≤10}={1,2,3,4,5,6,7,8,9,10},
A={1,2,4,5,9},B={4,6,7,8,10},C={3,5,7},
∴A∩B={4},
A∪B={1,2,4,5,6,7,8,9,10},
(CUA)∩(CUB)={3,6,7,8,10}∩{1,2,3,5,9}={3},
(CUA)∪(CUB)={3,6,7,8,10}∪{1,2,3,5,9}={1,2,3,5,6,7,8,9,10},
(A∩B)∩C={4}∩{3,5,7}=?,
(A∪B)∩C={1,2,4,5,6,7,8,9,10}∩{3,5,7}={5,7}.
解析分析:先用列举法求出全集U,然后利用集合的运算法则进行计算.

点评:本题考查集合的混合运算,难度不大,解题时要注意既不要重复,也不要遗漏.
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