4. Decide whether you think the following statement is true or false. If it is true, give a short explanation. If it is false, give a counterexample. Let G be an arbitrary flow network, with a source s, a sink t, and a positive integer capacity ce on every edge e. If f is a maximum s-t flow in G, then f saturates every edge out of s with flow (i.e, for all edges e out of s, we have f (e) = ce). 5. Decide whether you think the following statement is true or false. If it is true, give a short explanation. If it is false, give a counterexample. Let G be an arbitrary flow network, with a source s, a sink t, and a positive integer capacity ce on every edge e; and let (A, B) be a mimimum s-t cut with respect to these capacities {ce : e E). Now suppose we add 1 to every capacity; then (A, B) is still a minimum s-t cut with respect to these new capacities