Provide brief answers to the following questions. a. (2 marks) Define the complexity classes P and NP. b. (2 marks) Is it true that all problems in P are subset of NP (i.e., PC NP)? What about the converse? Please justify your answer. c. (3 marks) Is it true that if a NP-complete decision problem A reduces to some problem B in polynomial time, then B is also NP-complete? Please justify your answer. d. (3 marks) Let X be a problem that belongs to the class NP. Is it true that if X can be solved deterministically in polynomial time, then P = NP? Please justify your answer.