Let A and B be subsets of some universal set U. Prove that A = (A − B) ∪ (A ∩ B).
If you sub A - B , the same set members in both sets will be removed from A.
Then, if you add A ∩ B, that means that you will add into set A those members that are the same in both sets. Which means you subbed and then added the same thing. Hope this helps