Proving $f(C) \setminus f(D) \subseteq f(C \setminus D)$ and disproving equality Let $f: A\longrightarrow B$ be a function. 
1)Prove that for any two sets, $C,D\subseteq A$ , we have $f(C) \setminus f(D)\subseteq f(C\setminus D)$.
2)Give an example of a function $f$, and sets $C$,$D$, for which $f(C) \setminus f(D) \neq f(C\setminus D)$
First time exposed to sets.. how would I go about proving this? What assumptions should I make?


Here, $f: A \rightarrow B$ is in green and $\{S_i\} = S_i$ for $S = A, B$ and $i = 1, 2.$
Ignore $\{b_2\} = B_2$ in this picture. This picture proves that
$ f(A_1) - f(A_2) \neq f(A_1 - A_2)$. Incidentally, the same picture works for Is this proof correct for : Does $F(A)\cap F(B)\subseteq F(A\cap B) $ for all functions $F$?
