Q:

Explanation of $(x \notin A \setminus B)$

I don't understand  $(x \notin A \setminus B)$
Why is it not $$x \notin A \land x\in B$$ instead of $$x \notin A \lor x\in B$$

A:

We have that $x$ is not a member of the set $A$ \ $B$.
Expressing that in words, this means that $x$ is not a member of the bunch of things that specifically lives in $A$, but not in $B$. 
There are two ways in which this can happen. Either $x$ does not live in $A$ at all, or $x$ lives in $A$ but also lives in $B$.
Which is (after your edit) exactly what your last line says.

