Does it satisfy the criteria for a topology?

1) Does it include the empty set?

Yes.

2) Does it include X itself?

Yes.

3) If it includes set U and V does it include .

Since there are only 6 sets here, you could just check every possible intersection- yes, it does,.

4) Are all possible unions of members of the collection in the collection?

Again, there are only a finite number of unions to try- yes, it does.

So this is, in fact, a topology for X.