I am trying to write a proof to prove/disprove the following question:
Will it always be true that $f(W\setminus X) = f(W)\setminus f(X)$?
I know to prove this you need to show both ways since you have = sign. I have found a counterexample for $f(W\setminus X) \subseteq f(W)\setminus f(X)$. However, I know $f(W)\setminus f(X)\subseteq f(W\setminus X)$ is true, because I've been told it's true, but I don't understand how it's true and thus don't know how to write the proof for it. Could someone please explain why it's true/show how the proof would be written?