b) Any finite set.
c) The set of natural numbers.
d) The set of $\mathbb R-\mathbb Q$=irrational numbers.
I will appreciate your answers..
First, assume your teacher by interval meant any of the following kinds of intervals: $(a,b)$, $\ [a,b]$, $\ [a,b)$ and $(a,b]$.
(As an exercise, you should try to prove that each can be obtained by any fix kind of intervals, using countably infinite union and/or intersection of intervals of the fixed kind.)