SET PROBLEM

👨🏻‍🏫 學術台數學

explorer

2010-09-11 6:36 am

PROOF A cross ( B union C ) = ( A cross B ) union ( A cross C )

更新1:

係CROSS (X) 有是UNION !

更新2:

係CROSS (X) 不是UNION !

回答 (1)

myisland8132

2010-09-11 10:17 pm

✔ 最佳答案

x ∈ A ∩ (B ∪ C)
<=> x ∈ A and x ∈ (B ∪ C)
<=> x ∈ A and (x ∈ B or x ∈ C)
<=> (x ∈ A and x ∈ B ) or (x ∈ A and x ∈ C )
<=> x ∈ A ∩ B or x ∈ B ∩ C
<=> x ∈ (A ∩ B) ∪ (B ∩ C)

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