Prove that $$(A \cup B)−(A \cap B) = (A− B) \cup (B − A)$$ by showing that the left hand side is the subset of the right hand side and vice versa.

### Progress

Let $x$ be an element of LHS. Then x is an element of (A or B) and x is not an element of (A and B). So x is an element of (A or B) & negation of (A and B). Then I used laws to re-arrange it to get the right hand side. And did the same with the RHS.