The transitive reduction of a directed graph G (V, E) is a graph G-(V, E') on the same set of vertices, such that u and v are connected by a path in G if and only if u and v are also connected by a path in G', and no edge can be removed from G while prescrving this property. Show how to compute the transitive reduc- tion of a graph G in polynomial time. Can you also compute the number of distinct transitive reductions in polynomial time? (20 pts.)