Let http://alt2.artofproblemsolving.com/...3eae45b689.gif be a set with http://alt1.artofproblemsolving.com/...4b047a603d.gif elements. In how many different ways can one select two not necessarily distinct or disjoint subsets of http://alt2.artofproblemsolving.com/...3eae45b689.gif so that the union of the two subsets is http://alt2.artofproblemsolving.com/...3eae45b689.gif? The order of selection does not matter. For example, the pair of subsets http://alt2.artofproblemsolving.com/...44985a1495.gif represents the same selection as the pair http://alt1.artofproblemsolving.com/...846834bc7c.gif

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 http://alt2.artofproblemsolving.com/...32db70e8c4.gif. 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 http://www.artofproblemsolving.com/F...les/tongue.gif)