问题 选择题

设集合A={1,2,3,4,5,6},B={4,5,6,7,8},则满足S⊆A且S∩B≠∅的集合S的个数是(  )

A.57

B.56

C.49

D.8

答案

集合A的子集有:{1},{2},{3},{4},{5},{6},{1,2},{1,3},{1,4},{1,5},…,{1,2,3,4,5,6},∅,共64个;

又S∩B≠∅,B={4,5,6,7,8},

所以S不能为:{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3},∅共8个,

则满足S⊆A且S∩B≠∅的集合S的个数是64-8=56.

故选B

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