Let be a set with elements. In how many different ways can one select two not necessarily distinct or disjoint subsets of so that the union of the two subsets is ? The order of selection does not matter. For example, the pair of subsets represents the same selection as the pair

Firstly what does "two not necessarily distinct or disjoint subsets" mean?

And I've tried experimenting a bit. I wrote down the 16 different subsets for . There seems to be some pattern but I don't think brute force like this is the way to go...

So can someone explain an easier method? (Please don't leave out any steps cause I'm a beginner at combinatorics )