设全集U={X∈正整数|X≤8},若A交B的补集={2,8},A的补集并B的补集={1,2,3,4,5,6,7,8,}求集合A
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![设全集U={X∈正整数|X≤8},若A交B的补集={2,8},A的补集并B的补集={1,2,3,4,5,6,7,8,}求集合A](/uploads/image/z/949950-54-0.jpg?t=%E8%AE%BE%E5%85%A8%E9%9B%86U%3D%7BX%E2%88%88%E6%AD%A3%E6%95%B4%E6%95%B0%7CX%E2%89%A48%7D%2C%E8%8B%A5A%E4%BA%A4B%E7%9A%84%E8%A1%A5%E9%9B%86%3D%7B2%2C8%7D%2CA%E7%9A%84%E8%A1%A5%E9%9B%86%E5%B9%B6B%E7%9A%84%E8%A1%A5%E9%9B%86%3D%7B1%2C2%2C3%2C4%2C5%2C6%2C7%2C8%2C%7D%E6%B1%82%E9%9B%86%E5%90%88A)
设全集U={X∈正整数|X≤8},若A交B的补集={2,8},A的补集并B的补集={1,2,3,4,5,6,7,8,}求集合A
设全集U={X∈正整数|X≤8},若A交B的补集={2,8},A的补集并B的补集={1,2,3,4,5,6,7,8,}求集合A
设全集U={X∈正整数|X≤8},若A交B的补集={2,8},A的补集并B的补集={1,2,3,4,5,6,7,8,}求集合A
U={x∈正整数|x≤8}={1,2,3,4,5,6,7,8}
A∩CuB={2,8}
(CuA)∪(CuB)={1,2,3,4,5,6,7,8}
由摩根定律我们知道Cu(A∩B)=(CuA)∪(CuB)={1,2,3,4,5,6,7,8}
所以A∩B=空集
所以A=A∩U=A∩[(CuB)∪B]=[A∩B]∪[A∩CuB={2,8}]=空集∪{2,8}={2,8}
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