2. (20 points) Given a connected, weighted, and undirected graph G, answer True or False. If true, prove why, and if false, give a counter-example. (a) If e is a minimum-weight edge in G, it must be among the edges of at least one minimum spanning tree of G. (b) If e is a minimum-weight edge in G, it must be among the edges of every minimum spanning tree of the graph (c) If the edge weights in G are all distinct, then G must have ezactly one minimum spanning (d) If the edge weights of G are not all distinct, then G must have more than one minimum tree spanning tree