Let G = (V, E) be a connected, undirected graph where each edge e in E has an associated integer weight w(e). Let E be a subset of E that is contained in some minimum- weight spanning tree (MST) of G. (As in the lecture slides, we identify an MST (V, T ) of G with its edge set T , since the vertex set of any spanning tree of G is understood to be V .) Let G denote the subgraph (V, E) of G, and assume that G is not connected. Let (V1, E1) be a connected component of G, let E denote the set of all edges in E with exactly one endpoint in V1, and let e be a minimum-weight edge in E. Prove that some MST of G contains E + e. Remark: Your proof should not assume that the edge weights are distinct.