Let S = {1,2,,3,4}. The total number of unordered pairs of disjoint subsets of S is equal to

 S={1,2,3,4} Each element can be put in 3 ways either in subsets or
we don't put in any subset.
So total number of unordered pairs $=\frac{3\times 3\times 3\times 3-1}{2}+1=41$