3. A cut of an undirected graph G = (V, E) is a partition of its vertex set into two non-empty sets A, and B. An edge crosses the cut (A, B) if it has one endpoint in each of A and B. Assume G has pairwise distinct positive real-valued edge costs. Prove that if an edge e is the cheapest edge crossing a cut (A, B), then e belongs to every minimal nice tree of G.