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

Algebra ->  sets and operations -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Given problem is to prove %28B-A%29U%28C-A%29=%28BUC%29-A,
Let x be ∈ %28B+-+A%29+U+%28C+-+A%29

=> x ∈ %28B+-+A%29 or x ∈ %28C+-+A%29
= (x ∈ B and x ∉ A) or (x ∈ C and x ∉ A)
= (x ∈ B or x ∈ C) and (x ∉ A)
= (x ∈ B+U+C+) and (x ∉ A)
= x ∈ %28B+U+C%29+-+A
Hence proved %28B+-+A%29+U+%28C+-+A%29+=+%28B+U+C%29+-+A