Prove that in a bipartite graph G = (V, E) with two matchings M and M, where |M| < |M|, there exists a simple path P satisfying the following conditions: (1) Each edge in P belongs to either M or M but not both. (2) The first and last edges of P are both in M. (3) The endpoints of P are unmatched in M.

To find P, you can consider the symmetric difference of M and M, which is the set of edges that belong to exactly one of the two matchings.