Let $f$ be a function from $X$ to $Y$, and let $A$, $B$ be subsets (non-proper) of $X$. For each of the following statements, either prove the statement or else give a counter example:
a.) $f(X\setminus A)=Y\setminus f(A)$
b.) $f(X\setminus A) \subseteq Y\setminus f(A)$
c.) $Y\setminus f(A) \subseteq f(X\setminus A)$
d.) $f(A\cup B) = f(A)\cup f(B)$
e.) $f(A) \cap f(B) = f(A \cap B)$
I have an exam tomorrow and have been lagging on the set theory.
Much appreciated.