Let T1 and T2 be spanning trees of a connected graph G. (i) If e is any edge of T1, show that there exists an edge f of T2 such that the graph (T- {e})U {f} (obtained from T on replacing e by f) is also a spanning tree. (ii) Deduce that T1 can be 'transformed' into T2 by replacing the edges of T1 one at a time by edges of T2 in such a way that a spanning tree is obtained at each stage.

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