If $A \cap B = \emptyset$ then $A \subset B'$ and $B \subset A'$, where the prime symbol denotes the complement of each set.
Here are my thoughts:
Assume $A \cap B = \emptyset,$ since the intersection of $A$ and $B$ are empty, then an arbitrarily chosen element $x \notin A$ and $x \notin B.$ Thus $x \in A'$ and $x \in B'.$
How do I go about justifying that $A \subset B'$ and $B \subset A'?$
Maybe a direct proof is not the best way to do so? How about a proof by contradiction?
Thank you for any help or guidance!!!