Hello,

I need to prove that function defined like this $\displaystyle f:X->Y$ for any two given sets X,Y is one-to-one if and only if $\displaystyle f(A \cap B)= f(A) \cap f(B) $, where $\displaystyle A,B \subseteq X$.

What do I need to do to prove this?

EDIT:

I've figured out how to prove that $\displaystyle f(A \cap B)= f(A) \cap f(B) $ when f is injective. I still do not know how to conclude that f is injective when $\displaystyle f(A \cap B)= f(A) \cap f(B) $.