已知全集U={1,2,3,4,5,6,7,8,}集合A={3,4,5}B={4,7,8}验证Cu(A∩B)=CuAUCu
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2个回答

U={1,2,3,4,5,6,7,8},A={3,4,5},B={4,7,8}

A∩B = {3,4,5}∩{4,7,8} = {4}

Cu(A∩B) = U - (A∩B)

={1,2,3,4,5,6,7,8}-{4}

= {1,2,3,5,6,7,8}

and

CuA = U - A

= {1,2,3,4,5,6,7,8}-{3,4,5}

= {1,2,6,7,8}

CuB = U - B

= {1,2,3,4,5,6,7,8}-{4,7,8}

= {1,2,3,5,6}

CuAUCuB = {1,2,6,7,8}U {1,2,3,5,6}

= {1,2,3,5,6,7,8}

= Cu(A∩B) #

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