I was given an implication to prove, and I need to prove it using an indirect proof via contrapositive. I need to know the negation of this original statement: $A - B \subseteq C$. Presumably, I think it's $A - B \not\subseteq C$, but I'm not certain that $A - B \not\subseteq C$ is correct. The semantic of this statement is quite puzzling. Is it $\forall x \in A$, $\exists x \not\in B$, $\forall x \not\in C$? Does this mean $A - B$ and $C$ are disjoint sets when negated?