I don't know the logical expression for $\displaystyle \{x \in B|x \not \in C\}$.

I am thinking it could be one of these:

$\displaystyle \forall x(x \not \in c \rightarrow x \in B)$

or

$\displaystyle \forall x(x \in B \wedge x \not \in C)$

or

$\displaystyle

\forall x \in B (x \not C)$

Could you help?