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)$ ? 

$$A=(A \cap C)\cup(A-C)=(B \cap C)\cup(B-C)= B.$$
1st and last equality proved here, and the middle one is your assumptions.
