Show that f is surjective

So im having a little trouble proving this. Can anyone help me out?

Let $A$, $B subseteq E$.
Moreover, let $$f: mathscr{P}(E) to mathscr{P}(A) times mathscr{P}(B)$$ be defined by

$$f: X mapsto (A cap X, B cap X)$$

Show that $f$ is surjective iff $A cap B = emptyset$.

I’ve tried for a while to work out a proof, but I seem to be getting nowhere.

I’m new to set theory