Originally Posted by

**awkward** I'm going to assume that we consider

A={1}, B={1,2}

and

A={1,2}, B={1}

to be distinct cases.

How many ways are there to select two subsets without any restriction? Each element of {1, 2, ..., n} can be in

(1) neither A nor B,

(2) in A only,

(3) in B only, or

(4) in both A and B.

So there are 4^n ways to select A and B.

How many ways are there if A and B must be disjoint? We simply eliminate case (4) above. So there are 3^n ways to select A and B if they must be disjoint.

So the number of ways to select A and B if they must not be disjoint is 4^n - 3^n.