Question

Suppose a ⊆ c, and b and c are disjoint. prove that if x ∈ a then x ∈/ b.

Answer 1

If $x\in A$, then clearly $x\in C$. We're given that $B$ and $C$ are disjoint, so no element in $C$ is also in $B$. This means $x\not\in B$.