I'm sure I'm missing a small step somewhere, but I just don't know where. sorry, $X$ is a set. $A$ and $B$ are subsets of $X$
First assume $A=B$
Therefore: $X \setminus A = X-B$
Now assume $X setminus A=X-B$. I need to get $A=B$ from this assumption. I tried doing this:
Let $x\in(X-A)$; therefore $x$ is an element of $X$ but $x$ is NOT an element of $A$.
Let $y\in(X-B)$; therefore $y$ is an element of $X$ but $y$ is NOT an element of $B$.
Since $x=y$, conclude $A=B$.
Does this make sense?