A set $\displaystyle A$ is called an $\displaystyle F_\sigma$ set if it can be written as the countable union of closed sets. A set $\displaystyle B$ is called a $\displaystyle G_\delta$ set if it can be written as the countable intersection of open sets.

(a) Show that a closed interval [a, b] is a $\displaystyle G_\delta$ set.

(b) Show that the half open interval (a, b] is both a $\displaystyle G_\delta$ and an $\displaystyle F_\sigma$ set.

(c) Show that $\displaystyle Q$ is an $\displaystyle F_\sigma$ set, and the set of irrationals $\displaystyle I$ forms a $\displaystyle G_\delta$ set.

I have no idea where to start on this problem. Any help would be appreciated. Thank you for your time.