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I would really appreciate some help with this set proof.

1. The problem statement, all variables and given/known data

Show that, for any sets A, B, ((A ∪ B) ∩ A) = (A ∩ A') ∪ (A ∩ B).

(Hint: Remember that a complement of a complement is just the original set.)

2. Relevant equations

I can use any sentential calculus rules to prove this equality.

3. The attempt at a solution

I think that the key to this problem is to use the SC distribution rule. But using distribution on the left yields (A ∩ A) ∪ (A ∩ B), and I can't think of anyway to get the left side to (A ∩ A'). There is a hint with the question about complements of complements, but I don't see how to use that. I have tried variations of double negation and still cant get it started. If I can get the left side to ((A` ∪ B) ∩ A) before distribution that would work, but I'm not sure how to get there!

Thanks in advance for the help, I just need help getting this question started!

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# Proving a set theory equality

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