Show that $A \cap B$ is in $F$

Question

I just have a quick probability question.

Let $A$, $B$ be in $F$. Show that $A \cap B$ is in $F$ using $(A \cap B)^c$.

Any ideas on how I can solve this?

Answer 1

I assume you know that $F$ is closed under finite union and complementation. In that case, apply DeMorgan's laws as follows $$A\cap B = (A^c\cup B^c)^c.$$