Problem: MST

The following statements may or may not be correct. In each case, either prove it (if it is correct) or give a counterexample (if it isnt correct). Always assume that the graph G(V, E) is undirected. Assume that edge weights are distinct.

(a) If all edge weights are distinct, then the MST is unique.

(b) If graph G has more than |V| 1 edges, then the heaviest edge cannot be part of the minimum spanning tree. (c) If e E is part of some MST of G, then it must be a lightest edge across some cut of G. (d) If e is the lightest edge of a cycle of G, then e belongs to the MST.