Math: amounts and a proof about amounts

Question

I would like to proof or disprove the following 2 statements, if any is not true I need to find an example which disproves it.

X and Y are amounts and f: X --> Y

This is a question where I have trouble with. Can anyone give me an advice how to proceed here? It is on the first sheet of paper of homework as an additional question, but anyhow I would like to understand it. I am not familiar with english notations, please adjust my tags and headline if needed.

Answer 1

Here's an example disproving one of the equalities. Let $X=\{1,2,3\}$, $A=\{1,2\}$. Let $Y=\{p,q,r\}$ Define $f$ by $f(1)=p$, $f(2)=q$, $f(3)=p$.

Then $f^{-1}(f(A))=f^{-1}(\{p,q\})=\{1,2,3\}\ne A$.