(Graph Connectivity - Menger's Theorem) Let s and t be two nodes in a directed graph. Use the max-flow/min-cut theorem to show that:
(a) The maximum number of forward paths from s to t that do not share any arcs is equal to the minimum number of arcs that when removed from the graph, eliminate all forward paths from s to t.
(b) The maximum number of forward paths from s to t that do not share any nodes (other than s and t) is equal to the minimum number of nodes that when removed from the graph, eliminate all forward paths from s to t.
