A set is called an set if it can be written as the countable union of closed sets. A set is called a set if it can be written as the countable intersection of open sets.

(a) Show that a closed interval [a, b] is a set.

(b) Show that the half open interval (a, b] is both a and an set.

(c) Show that is an set, and the set of irrationals forms a set.

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