Finding if two sets are equal I have an formula 
$(A\cap C) \cup ( B \cap  C) = C - ( A \cap B)$
and i have to prove if this equation is correct.
I transformed it into
$(\forall x\in U: x \in A \wedge x\in C) \vee ( x\in B\wedge x\in C) = x \in C \wedge ( x \notin A \wedge  x\notin B)  $
how could i further transform the equations in order to find if its true or not?

Instead of transforming the equation just go after the english meaning: those  in A and C or B and C are those in C but not both A and B. This is obvioyusly not true: Consider A=B
