A vital arc of a network is an arc whose removal from the network causes the shortest distance between two specified nodes, say nodes and node t, to increase. A most vital arc is a vital arc whose removal yields the greatest increase in the shortest distance from node s to node t. Assume that the network is directed, arc lengths are positive, and some arc is vital. Prove that the following statements are true or show through counterexamples that they are false. (a) A most vital arc is an arc with the maximum value of cy. (b) A most vital arc is an arc with the maximum value of c on some shortest path from node s to node t. (c) An arc that does not belong to any shortest path from node s to node t cannot be a most vital arc. (d) A network might contain several most vital arcs.