Let $A$ and $B$ be sets. Show that $(A\cup B)-(A\cap B)=A$ then $B=\emptyset$
I know I have to use a proof by contradiction, so I should assume there exists a $b$ that is an element of $B$. But I am not sure where to go from there. Also, should this expression be equal to elements found in both $A$,$B$ and not just $A$.
Rewrite your equation as A = (A - B) $\cup$ (B - A).
Assume exists x in B.
Case x in A. So either x in A - B or x in B - A.
Case x not in A, So x in B - A.
In both cases, derive a contradiction.