(a) Consider the directed network below, whose edge capacities are indicated. For each of the vertex sets \(\{1,2\},\{1,2,3\}\), and \(\{1,4\}\), list the edges in the cut corresponding to the set and compute the capacity of the cut.

(b) Assume it is the case that the vertex set \(\{1,2\}\) determines a minimum cut. Use your intuition to find a maximum flow without executing the algorithm (Hint: see Lemma 2).

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Exercise 1 1 M 3 Exercise 2