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( )
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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
A. 57
B. 56
C. 49
D. 8
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1+
C16+
C26+
C36+
C46+
C56+
C66=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.
C16+
C26+
C36+
C46+
C56+
C66=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.
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( )
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