Question 8
Let $S$ be a set with six elements. In how many different ways can one select two not necessarily distinct subsets of $S$ so that the union of the two subsets is $S?$ The order of selection does not matter; for example, the pair of subsets $\{a,c\},$ $\{b,c,d,e,f\}$ represents the same selection as the pair $\{b,c,d,e,f\},$ $\{a,c\}.$