How would you write $A\setminus(B\setminus C)$? I know that $(A \setminus B) = \{x: x \in A$ and $x \not \in B)\}$, but am not sure how to write $A\setminus(B\setminus C)$ in the same form.

$A - (B - C)$ is the set of all elements in $A$ which are not in $B - C$. $B - C$ is the set of all elements in $B$ that are not in $C$. Thus $A$ consists of all $x$ such that $x \in A$, and $\neg (x \in B\ \text{and}\ x \not \in C)$. You can make this nicer using Boole's identities. I leave this for you to finish (I assume this is a homework problem, so its good practice to complete it yourself). 
