Question: (a) Let (S, V S) be a minimum cut in network G. Let (u, v) be an edge such that u ES and ve (V-S).

(a) Let (S, V S) be a minimum cut in network G.

(a) Let (S, V S) be a minimum cut in network G. Let (u, v) be an edge such that u ES and ve (V-S). It is claimed that increasing the capacity of the edge (u, v) will increase the maximum flow in G. Prove the claim or provide a counterexample. (b) Let f denote the maximum flow of some network G. We then increase the capacity of every edge by 1. It is claimed that the maximum flow in this modified network will be at most f +1. Prove the claim or provide a counterexample. (a) Let (S, V S) be a minimum cut in network G. Let (u, v) be an edge such that u ES and ve (V-S). It is claimed that increasing the capacity of the edge (u, v) will increase the maximum flow in G. Prove the claim or provide a counterexample. (b) Let f denote the maximum flow of some network G. We then increase the capacity of every edge by 1. It is claimed that the maximum flow in this modified network will be at most f +1. Prove the claim or provide a counterexample

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