Question

一道高一的关于集合的数学题！

U={1,2,3,4},若A∪B=U,A∩B不等于空集，且A∩B的补集={1,2}，试写出满足上述条件的集合A、B所有！！

Answer 1

A∪B=U={1,2,3,4}, Cu(A∩B)= {1,2}

Cu (A∩B) = U - (A∩B)
{1,2 }= {1,2,3,4} - (A∩B)
(A∩B) = {3,4}
AUB = {1,2,3,4}

A = {1,2,3,4}, B={3,4}
A = {2,3,4}, B={3,4}
A = {2,3,4}, B={1,3,4}
A = {1,3,4}, B={3,4}
A = {1,3,4}, B={2,3,4}
A = {3,4}, B={1,2,3,4}
A = {3,4}, B={1,3,4}
A = {3,4}, B={2,3,4}
A = {3,4}, B={3,4}

Answer 2

A={1,2,3,4},B={1,2,}

Answer 3

A交B不等于空集，则A、B均不是空集，且A、B中不含1和2，所以
A={3} B={3}
A={3} B={4}（此时A交B为空，不是空集，空和空集是两个概念）
A={3} B={3,4}
A={4} B={3}
A={4} B={4}
A={4} B={3,4}
A={3,4} B={4}
A={3,4} B={3}
A={3,4} B={3,4}