Originally Posted by

**Ackbeet** I think you need to clean up your work a bit. You're trying to show that

$\displaystyle (A-B)\cup(B-A)=(A\cup B)-(A\cap B).$

Incidentally, both sides of this equation represent the symmetric difference of $\displaystyle A$ and $\displaystyle B$.

What you need to show is that each side is a subset of the other. The statement you wrote

is incorrect. The correct statement would be

For the forward direction, you start out correctly:

But then you say this:

That is incorrect. It should be this:

Can you continue from here, or are you still stuck?