Let n 2, and let A12 A2 2... 2 An be a finite nested sequence of sets. Show that all of the following are equivalent (i.e., each implies the others): (i) The family {A} is pairwise intersecting. . (ii) The family is not mutually disjoint: 1 Ai (iii) The set An is nonempty. Find a nested infinite sequence of subsets of R A 24 2... 2 An 2... that is pairwise intersecting but mutually disjoint: -1 An = 0.