Prove that in set theory $A-B = A - (A \cap B)$ Prove that in set theory $A-B = A - (A \cap B)$
Please give me a hint.
Let $x\in A-B \implies x\in A~ and ~x \notin B\implies x\in A ~and (x\in A ~and~ x \notin B)\implies x\in A - (A \cap B)$

Let $x \in A - B$. Then, $x$ is in $A$, but $x$ is not in $B$. It follows that $x$ is not in both $A$ and $B$, otherwise $x$ would be in $B$. Hence, $x \in A - (A \cap B)$, so $A-B \subset A - (A\cap B)$. Can you do the other direction using this as a model?
