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

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/08 11:12:05

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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