6. LetXbe a non-empty set containing at least two elements, and let a and b be fixed

but different points in X.

(a) Show that the family T = {U ∈ PX | a ∈ U} ∪ {∅} is a topology on X.

(b) Is the family T = {U ∈ PX | a ∈ U or b ∈ U} ∪ {∅} a topology on X?

I don't get this question, what are they asking for, is T the Discrete Topology???(Angry)