Final answer:
Assuming x is in A-C leads to a contradiction with the fact that A ∩ B is a subset of C, thus proving the initial statement incorrect by contradiction.
Step-by-step explanation:
Proving that if A ∩ B \subseteq C and x \in B, then x \\otin A-C can be approached by proof of contradiction. Let's assume the opposite of what we're trying to prove; that is, assume that x \in A-C. This assumption implies that x \in A and x \\otin C. However, because we know that A ∩ B \subseteq C, and since x \in B, it would follow that x should be in C (as it belongs to the intersection of A and B which is a subset of C). This is a contradiction, as our initial assumption leads to x both being in C and not in C at the same time, which is not possible. Hence, by this contradiction, it follows that x cannot be in A-C, proving our initial statement.