设全集U={x∈N/2≤x≤30},集合A={x/x=2n,n∈N+,且n≤15},B=｛x/x=3n+1,n∈N+,且n≤9｝,C=｛x/x是小于

题目

设全集U={x∈N/2≤x≤30},集合A={x/x=2n,n∈N+,且n≤15},B=｛x/x=3n+1,n∈N+,且n≤9｝,C=｛x/x是小于
30的质数｝,则[Cu(A∪B）]∩C=————————,

答案

因为A={x/x=2n,n∈N+,且n≤15} 所以A={2,4,6,8,10,12,14,16,18,20,22,24,26,28,30};因为B=｛x/x=3n+1,n∈N+,且n≤9｝,所以B=｛4,7,10,13,16,19,22,25,28｝,所以A∪B={2,4,6,7,8,10,12,13,14,16,18,19,20,22,24,25,26,28,30},所以Cu(A∪B）={3,5,9,11,15,17,21,23,27,29},因为C=｛x/x是小于30的质数｝,所以C={2,3,5,7,11,13,17,19,23,29},所以[Cu(A∪B）]∩C={3,5,11,17,23,29}