By contracting an edge e = uv, we mean removing e and identifying the vertices u and v as a single new vertex. Let num_T(G) denote the number of spanning trees of the graph G.

a. Show that the following recursive formula holds:
num_T(G) = num_T(G - e) + num_T (G * e)
where G * e means the multigraph obtained from G by contracting the edge e.

b. Give a counterexample if multiple edges are identified to make G * e into a graph.