Show that the equivalence of Konig's Theorem and Hall's marriage theorem:

Konig's Theorem: Let G be a bipartite graph. The size of a maximum matching of G is equal to the size of a minimum covering of G.

Hall's marriage theorem: A bipartite graph G with vertex sets V1 and V2 contains a complete matching from V1 to V2 if and only if it satisfies Hall's condition |(S)| |S| for every S V1.