(c) State and prove Hall’s Theorem

Hall’s Theorem is a fundamental result in combinatorics and graph theory, specifically in the context of bipartite graphs. It provides a necessary and sufficient condition for the existence of a perfect matching in a bipartite graph.

Hall’s Theorem:

Let G=(X,Y,E)G = (X, Y, E) be a bipartite graph where XX and YY are disjoint sets of vertices, and EE is the set of edges between __________ _____ ____ ______ _______ ___ ____ _________ __________ _________ ______.
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