Enumerative Combinatorics

A detailed proof with explanations will be appreciated

Let n E N. How many (ordered) pairs (A, B) of two nonempty subsets of [n] have the property that min A > [B) and min B > (A) ? [Example: If n = 7, then the pair ({3, 5, 7} , {4, 5} ) qualifies, since min {3, 5, 7} = 3> 2 = 1{4, 5}| and min {4, 5} = 4 > 3 = |{3,5, 7}|. However, the pair ({2, 5, 7} , {4, 5}) does not qualify, since min {2, 5, 7}