化简下列集合表达式

题目

化简下列集合表达式
(1)(B-(A∩C))∪(A∩B∩C)
(2)(A∩B)-(C-(A∪B))
(3)((A∪B)∩B-(A∪B)
(4)((A∪(B∪C))-(B∪C))∪A

答案

(1)原式 = (AC) + BAC = B[~(AC) + AC] = B(2)原式 = AB~(C~B) = AB(~C + A + B) = AB~C + AB + AB = AB(3)原式 = (A + B)B~(A + B) = (AB + B)~B = B = 0(4)原式 = (A + B + C)~(A + B + C) = 0其中,A表示“A的非”...