Let \mathcal{S} be the set \{1,2,3, \ldots, 10\}. Let n be the number of sets of two non-empty disjoint subsets of \mathcal{S}. (Disjoint sets are defined as sets that have no common elements.) Find the remainder obtained when n is divided by 1000 .
Let \mathcal{S} be the set \{1,2,3, \ldots, 10\}. Let n be the number of sets of two non-empty disjoint subsets of \mathcal{S}. (Disjoint sets are defined as sets that have no common elements.) Find the remainder obtained when n is divided by 1000 .