1. The problem statement, all variables and given/known data Let A and B be sets. Prove that A U B=(A-B) U (B-A)U (A∩B) 2. Relevant equations 3. The attempt at a solution If I want to prove the foward direction: A U B⊆(A-B) U (B-A)U (A∩B) then from my understanding I know that xεA or xεB. And I can assume wolog that xεA. But since I assume that x is an element from A, its already equal to (A-B) U (B-A)U (A∩B)? Since xεA and x is not an element of B or xεb and not an element of A or x is both an element of A and B? is that all i have to show for the foward direction?