化简下述集合公式(离散数学) (A∩B∩C)∪(A∩~B∩C)∪(~A∩B∩C)
问题描述:
化简下述集合公式(离散数学) (A∩B∩C)∪(A∩~B∩C)∪(~A∩B∩C)
答
(A∩B∩C)∪(A∩~B∩C)∪(~A∩B∩C)
=(A∩B∩C)∪(A∩B∩C)∪(A∩~B∩C)∪(~A∩B∩C)
=[(A∩B∩C)∪(A∩~B∩C)]∪[(A∩B∩C)∪(~A∩B∩C)]
=(A∩C)∪(B∩C)
=(A∪B)∩C