Problem 3. Let (u, v) be a minimum-weight edge in a connected graph G. Show that (u, v) belongs to some minimum spanning tree of G.

Consider a connected graph G with at least 4 edges that has all distinct edge weights. Which of the following properties must be true of a Minimum Spanning Tree (MST) of G? I. The MST must contain the shortest edge of G. II. The MST must contain the second-shortest edge of G. III. The MST can never contain the longest edge of G. None I Only I and II Only I and III Only O1, II, and III

[Alg 2018 1] Please this question step by step

Let G = (V, E) be a connected graph that has two distinct spanning trees. Prove that |E| > |V] – 1.