Find the relations between A, B and C when $[(A\cap B)\cup C]-A=(A\cap B)-C$
So we can write it as: $[(A\cup C)\cap(B\cup C)]-A=(A\cap B)-C$. Here comes the problem, though. Can I just assume that $[(A\cup C)\cap(B\cup C)]=(A\cap B)$? If I can, I can go on from there with: $C\subseteq A, C\subseteq B$ and eventually for the whole thing to hold $A=C$ which then shows that $A\subseteq B$. Can I do this that way, however? I feel that I'm assuming too much by simply comparing $[(A\cup C)\cap(B\cup C)]$ and $(A\cap B)$ to each other.