How to proof ?Any ideas would be useful.
A\(BUC) = (A\B) ∩ (A\C)
x are A\(BUC) => (x arenít (A)) and (x are (BUC)) => (x arenít (AUA)) and (x are (BUC)) => (x arenít (A)) or (x are (B∩C)) => ((x arenít A) or (x are B)) and ((x arenít A) or (x are C)) => (x are (A\B)) and (x are (A\C)) => x are ((A\B) ∩ (A\C))
What you did required some sort of knowledge of what was actually going on, or at least someone telling you some rules. The other two ways don't.
I've never been able to derive proofs just using what I know about sets...I prefer to either look at an element or draw a diagram.