SOLUTION: Hello, my question is about proving a set identity: Prove (B - A) U ( C-A ) = ( B U C) - A. I know that I must show (B - A) U ( C-A ) is a subset of ( B U C)

SOLUTION: Hello, my question is about proving a set identity: Prove (B - A) U ( C-A ) = ( B U C) - A. I know that I must show (B - A) U ( C-A ) is a subset of ( B U C) - A and ( B U

Question 1140918: Hello, my question is about proving a set identity:
Prove (B - A) U ( C-A ) = ( B U C) - A.
I know that I must show (B - A) U ( C-A ) is a subset of ( B U C) - A and ( B U C) - A is a subset of (B - A) U ( C-A ), but I am confused on how I should do this.
I would appreciate some help please.
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
Given problem is to prove ,
Let be ∈

=> ∈ or ∈
= ( ∈ and ∉ ) or ( ∈ and ∉ )
= ( ∈ or ∈ ) and ( ∉ )
= ( ∈ ) and ( ∉ )
= ∈
Hence proved

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