Proof on set equality I was making a few exercises on set proofs but I met an exercise on which I don't know how to start:

If $A \cap C = B \cap C $ and $ A-C=B-C $ then $A = B$

Where should I start? Should I start from $ A \subseteq B $ or should I start from this $ ((A\cap C = B\cap C) \land  (A-C = B-C)) \Rightarrow (A = B)$ ? 

You show $A\subseteq B$ and $B \subseteq A$, as one usually would when showing that two sets are equal. Since the conditions are symmetric in $A$ and $B$, the two proofs are completely analoguous, so I will only do one of them.
To show $A \subseteq B$, take an $a \in A$, and note that either $a \in C$ or $a \notin C$. If $a \in C$, then we have $a \in A\cap C$. If $a\notin C$, then we have $a \in A-C$. In both cases, you may use the given set equalities to conclude that $a \in B$. This shows $A \subseteq B$.
