Question

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

Answer 1

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) #