Complete the following steps in an inductive proof of the correctness of Prim's algorithm on a graph G=(V, E), V = n. Proof. Let P(k) be the statement "at step k of Prim's algorithm, the current tree Tk with k vertices and k-1 edges is part of a MST of G". The statement Pn) therefore says that Prim's algorithm returns an MST (since the tree T(n) must also be a spanning tree). Basis step: (k = 1): Inductive Step: Let 1