设集合A={x|0<x<9,x是质数},B={x|0<x<9,x∈N},则满足条件A?S⊆B的集合S共有( )个.
A.7
B.8
C.15
D.16
【答案】分析:根据质数和自然数的定义,可以用列举法表示出集合A={x|0<x<9,x是质数},B={x|0<x<9,x∈N},进而列举出所有满足条件A?S⊆B的集合S,即可得到答案.
解答:解:∵集合A={x|0<x<9,x是质数}={2,3,5,7},
B={x|0<x<9,x∈N}={1,2,3,4,5,6,7,8},
又∵集合S满足条件A?S⊆B
∴S={1,2,3,5,7},或S={2,3,4,5,7},或S={2,3,5,6,7或},或S={2,3,5,7,8},
或S={1,2,3,4,5,7},或S={1,2,3,5,6,7},或S={1,2,3,5,7,8},
或S={2,3,4,5,6,7},或S={2,3,4,5,7,8},或S={2,3,5,6,7,8},
或S={1,2,3,4,5,6,7},或S={1,2,3,4,5,7,8},或S={1,2,3,5,6,7,8},
或S={2,3,4,5,6,7,8},或S={1,2,3,4,5,6,7,8},
故满足条件的集合S共有15个
故选C
点评:本题考查的知识点是集合的包含关系判断及其应用,其中根据质数和自然数的定义,可以用列举法表示出集合A和集合B是解答本题的关键.