1644 A Let S be a finite set and let S, S2.... . St be a partition of S into nonempty disjoint subsets. Define the structure (S,1) by the condition that I = {A: IA n Sil 1 for i = 1, 2, ,k]. Show that (S,I) is a matroid. That is, the set of all sets A that contain at most one member of each subset in the partition determines the independent sets of a matroid