U={x|x=2n-1,n∈n+,n小于等于7},A∩(CuB)={3,7},Cua∩B={9,13},CuA∩CuB={1,11},求A,B

题目

U={x|x=2n-1,n∈n+,n小于等于7},A∩(CuB)={3,7},Cua∩B={9,13},CuA∩CuB={1,11},求A,B

答案

U={x|x=2n-1,n∈n+,n小于等于7}=｛1,3,5,7,9,11,13｝
A∩(CuB)={3,7}得3,7属于A,不属于B
Cua∩B={9,13}得9,13属于B,不属于A
CuA∩CuB={1,11}得A∪B=｛3,5,7,9,13｝
可得A=｛3,7｝或｛3,5,7｝,B={9,13}或｛5,9,13｝
又,当A=｛3,7｝,B={9,13}时,A∪B≠｛3,5,7,9,13｝（舍）
当A=｛3,5,7｝,B={9,13}时,A∩(CuB)={3,5,7}≠{3,7}（舍）
当A=｛3,7｝,B=｛5,9,13｝时,Cua∩B={5,9,13}≠｛9,13｝（舍）
故A=｛3,5,7｝,B=｛5,9,13｝