Ok I made an attempt to answer this question. I would like for someone to check it to see if I'm on the right track.
Suppose $A,B$ are sets and that $A\setminus B = A\oplus B$. Prove $B\subseteq A$. (btw, $\oplus$ represents symmetric difference).
Proof: Let $x$ be an element of $A$. Let $x$ also be an element of $B$. Therefore, $x$ is not an element of $A\setminus B$ and since $A\setminus B = A\oplus B$, $x$ is not an element of $A\oplus B$ either. Thus, $B$ is a subset of $A$.
I'm not sure if that is correct, but could someone double check it for me?