Prove A \ (A ∩ B) = (A ∪ B) \ B

Question

My question states: Given sets A and B, show that A \ (A ∩ B) = (A ∪ B) \ B.

This is where I got to before I got stuck: $$x \; \in \; A \; \setminus \; (A∩B)$$ $$x \; \in \; A \quad and \quad \notin \; (A∩B)$$ $$x \; \in \; A \quad and \quad (x \notin A \; or \; x \notin \; B)$$ $$ x \; \in \; A \quad and \quad x \; \notin \; B$$

Answer 1

....

$x \in A$ and $x \not \in B$

($x \in A$ or $x \in B$) and $x\not \in B$

$x \in (A\cup B)\setminus B$.

$A\setminus(A\cap B) \subset (A\cup B)\setminus B$

..........

And if

$x \in (A\cup B) \setminus B$ then

($x\in A$ or $x \in B$) and $x \not \in B$

$x\in A$ and $x \not \in B$

$x\in A$ and ($x \not \in A$ or $x\not \in B$)

$x\in A$ and $x \not \in A\cap B$

$x \in A\setminus (A\cap B)$.

$A\setminus(A\cap B) \supset (A\cup B)\setminus B$

So

$A\setminus(A\cap B) = (A\cup B)\setminus B$