Is the following statement true or false? Provide a proof or counter example.
"For any function $f: X \rightarrow Y$, and any subset $A$ of $X$, we have $$f(A \cap (X\backslash A)) = f(A) \cap f(X\backslash A)$$
I think this is false because how can some element be in a set and also not be in its set. But I'm not sure