g Let X be a problem that is in the class NP . For each of the following write if it is " True," "False," or "We don’t know." Justify your answer. (a) Solutions to X can be verified with a polynomial - time algorithm. (b) There is no polynomial - time algorithm for X . (c) If there exists a polynomial - time algorithm for X , then P = NP . (d) If there exists a polynomial - time algorithm for X , then there m ust exist a polynomial - time algorithm for the Traveling Salesman Problem. (e) If there exists a polynomial - time algorithm for the Traveling Salesman Problem, then there must exist a polynomial - time algorithm for X .