Let G be a bipartite graph, with bipartition (A, B). Show that the following are equivalent: (i) there is a matching M in G so that every vertex in A is an end of some member of M (ii) for every X C A there are at least |X vertices in B with a neighbour in X. Let G be a bipartite graph, with bipartition (A, B). Show that the following are equivalent: (i) there is a matching M in G so that every vertex in A is an end of some member of M (ii) for every X C A there are at least |X vertices in B with a neighbour in X