(A∪B)∩(A∪B∪C)∩(Ac)

( A ∪ B ) ∩ ( A ∪ B ∪ C ) ∩ ( Aᶜ )
=
( A ∪ B ) ∩ ( Aᶜ ) ........ ∵ M ∩ ( M ∪ C ) = M is A ∪ B , [absorption law]
=
B \ A


圖片參考：http://www3.wolframalpha.com/Calculate/MSP/MSP10231a330gffdcad55gb000017de88eh30289f11?MSPStoreType=image/gif&s=12&w=185&h=178&cdf=Resizeable



Alternatively :( A ∪ B ) ∩ ( A ∪ B ∪ C ) ∩ ( Aᶜ )
=
( A ∪ B ) ∩ (B ∪ C ) \ A
=
B ∩ (B ∪ C ) \ A
=
B \ A

2012-09-10 01:37:16 補充：
( A ∪ B ) ∩ ( A ∪ B ∪ C ) = A ∪ B (兩方有 A ∪ B , 交集便是A ∪ B)

於是原題等同
(A ∪ B) ∩ ( Aᶜ )
= B ∩ Aᶜ (因 A ∩ Aᶜ 是空集 , 消去A)
= B \ A (B集中所含的A集元素 ∩ Aᶜ 是空集 , 故從B中消去A)

2012-09-10 01:37:58 補充：
( A ∪ B ) ∩ ( A ∪ B ∪ C ) = A ∪ B (兩方有 A ∪ B , 交集便是A ∪ B)

於是原題等同
(A ∪ B) ∩ ( Aᶜ )
= B ∩ Aᶜ (因 A ∩ Aᶜ 是空集 , 消去A)
= B \ A (B集中所含的A集元素 ∩ Aᶜ 是空集 , 故從B中消去A)