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

问题描述:

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

A∩B={4},
Cu(A∩B)={1,2,3,5,6,7,8}
CuA={1,2,6,7,8,};
CuB={1,2,3,5,6}
CuAUCuB)={1,2,3,5,6,7,8}
所以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} andCuA = U - A= {1,2,3,4,5,6,7,8}-{3,4,5}= {1,2,6,7,8...