4. P, NP, and NP-Complete. Assume that computer scientists have proven that P is not equal to NP. CIRCLE either TRUE, FALSE or UNKNOWN (i.e. statement is still unknown to computer scientists even in light of this proof) given this assumption. (a) P is not equal to NP. TRUE FALSE UNKNOWN (b) There does not exist an efficient algorithm for finding the non-trivial integer prime factors of a number (FACTOR). TRUE FALSE UNKNOWN (c) The traveling salesperson problem (TSP) is not in P. TRUE FALSE UNKNOWN (d) The "Is this list sorted?" decision problem is not in NP. TRUE FALSE UNKNOWN (e) There exists an efficient algorithm for finding optimal TSP tours, but no one has been able to find it. TRUE FALSE UNKNOWN (f) SAT poly-time reduces to SORT. TRUE FALSE UNKNOWN (g) No algorithm can guarantee to efficiently find an optimal tour for TSP. TRUE FALSE UNKNOWN (h) One can construct a program that accepts an integer N, efficiently produces a single TSP of size N of its choice, and efficiently computes that TSP's optimal tour. TRUE FALSE UNKNOWN (i) There does not exist an efficient algorithm for the Boolean satisfiability problem. (SAT) TRUE FALSE UNKNOWN