Q:

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:

Consider that $~x\notin B~$ is $~\neg(x\in B)~$.
So you can write: $~A\setminus B= \{x: x\in A\wedge \neg (x\in B)\}~$.
Likewise you can write: $~A\setminus (B\setminus C) = \{x: x\in A \wedge \neg(x\in B\wedge \neg (x\in C)) \}~$.
So, with a little dual negations: $$A\setminus (B\setminus C) = \{x: x\in A \wedge (x\notin B\vee x\in C) \}$$

