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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?

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It would help us if you explained what $F$ is, and what definition you are using for $F$ (i.e. closed under unions and complements, or something along those lines), what you have tried, etc. – Jason Polak Oct 1 '12 at 1:23
up vote 3 down vote accepted

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

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