Question: Consider the Minimum Spanning Tree Problem on an undirected graph G =( V , E ), with a cost c e 0 on each edge,

Consider the Minimum Spanning Tree Problem on an undirected graph G=(V,E), with a cost ce 0 on each edge, where the costs may not all be different. If the costs are not all distinct, there can in general be many distinct minimum-cost solutions. Suppose we are given a spanning tree T E with the guarantee that for every e T, e belongs to some minimum-cost spanning tree in G. Can we conclude that T itself must be a minimum-cost spanning tree in G? Give a proof or a counterexample with explanation.

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