Prove that a bipartite graph G = (X, Y, E) has a matching of size t if and only if for all A in X, |R(A)| lessthanorequalto |A| + t - |X| = t - |X - A|. Let Delta(G) = max_ A SubsetEqualto X (|A| - |R(A)|. Delta (G) is called the deficiency of the bipartite graph G = (X, Y, E) and gives the worst violation of the condition in Theorem 2. Note that Delta (G) lessthanorequalto 0 because A = phi is considered a subset of X. Use Exercise 16 to prove that a maximum matching of G has size |X| - Delta (G)