Using properties of sets, show that for any two sets A and B, (A ∪ B) ∩ (A ∪ B’) = A.
We need to show (A ∪ B) ∩ (A ∪ B’) = A.
Now,
(A ∪ B) ∩ (A ∪ B’) = ((A ∪ B) ∩ A) ∩ B’.
= (A ∩ A) ∪ (B ∩ A)) ∩B’
= A ∩ B’
= A.