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)=CuAUCuB
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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