Consider a flow network G = (V, E, s, t,c) with at least 5 edges. Prove or disprove the following statements. (a) (4 points) Suppose that we decrease the capacity of a certain edge e E E. This decreases the max flow value if and only if e belongs to any min-cut in G. This decreases the max flow value if and only if e belongs to every min-cut in G. Consider a flow network G = (V, E, s, t,c) with at least 5 edges. Prove or disprove the following statements. (a) (4 points) Suppose that we decrease the capacity of a certain edge e E E. This decreases the max flow value if and only if e belongs to any min-cut in G. This decreases the max flow value if and only if e belongs to every min-cut in G