If you could help me out with this I will be so glad. I have been tring to come up with some proof, but I haven't found one yet. 

Let $X$ and $Y$ be sets, and let $f : X \to Y$ be a function defined in $X$ with values in $Y$. Prove that if $A,B \subset Y$; then
$$f^{-1}(A \setminus B) = f^{-1}(A) \setminus f^{-1}(B)$$