Proving $A \subset B \Rightarrow B' \subset A'$ Suppose that A is a subset of B. How can we show that B-complement is a subset of A-complement?

Instead of using a proof by contradiction, $b\in B^c \implies b \notin A$ since $A \subset B$ hence $b \in A^c$ which implies the result.
The key here being that for all $x$, either $x\in X$ or $x\in X^c$.
