2.12
举一个例子,解决两个小题
A={1,2}
B={2,3}
(1)
A-B={1}
(A-B)∪B={1,2,3}≠A
(2)
A∪B={1,2,3}
(A∪B)-B={1}≠A
2.13
(1)
(A⋂B)∪(C⋂D)
=(A∪(C⋂D))⋂(B∪(C⋂D))
=(A∪C)⋂(A∪D)⋂(B∪C)⋂(B∪D)
(2)
A1⋂(-A1∪A2)
=(A1⋂-A1)∪(A1⋂A2)
=∅∪(A1⋂A2)
=A1⋂A2
A1∪(-A1⋂A2)
=(A1∪-A1)⋂(A1∪A2)
=U(全集)⋂(A1∪A2)
=A1∪A2
(3)题目有误,可以举反例A=B=C=∅,显然等式结论不成立(等式左边=∅,右边是全集):
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