Suppose $A$, $B$, and $C$ are sets, and $A - B \subseteq C$. Then $A - C \subseteq B$. I know how to prove it by contradiction, but I am wondering if it's possible to prove it directly. I tried doing that, but so far no results. Is it not possible to prove it directly?
Thanks.

Let $a\in A-C$, then $a\in A$ and $a\notin C$. Therefore $a\notin A-B$. So either $a\notin A$ or $a\in B$. Since $a$ Was taken from $A$, we have that $a\in C$ as wanted.
