4. (20 points) Ans wer the following questions. Either prove it or give a counter-example (a) D oes th along edges from source to target? e maximum flow problem always have a unique solution in terms of the flows (b) D oes the maximum flow problem always have a unique solution in terms of the flows along edges from source to target if all edge capacities are different (c) D oes the minimum cut problem have a unique solution in terms of the actual (S, T) cut? (d) Does the minimum cut problem have a unique solution in terms of the actual (S, T) cut if all edge capacities are different? 4. (20 points) Ans wer the following questions. Either prove it or give a counter-example (a) D oes th along edges from source to target? e maximum flow problem always have a unique solution in terms of the flows (b) D oes the maximum flow problem always have a unique solution in terms of the flows along edges from source to target if all edge capacities are different (c) D oes the minimum cut problem have a unique solution in terms of the actual (S, T) cut? (d) Does the minimum cut problem have a unique solution in terms of the actual (S, T) cut if all edge capacities are different