1. Prove the following entailment in SD. PQ, P →REP→ (Q ^ R)

How many different onto functions f: S→ T can be defined that map the domain S = {1, 2, 3,..., 10} to the range T = {11, 12, 13,..., 20}? Enter your answer in the box below. Answer =

Question 2: Let f (x):R→R, f(x) = 2x2 +5. a. Is f(x) one-to-one? Prove your answer. b. Is f(x) onto? Prove your answer. c. Is f(x) bijection? Prove your answer. d. Does f(x) have inverse function? If so, find f -(x) and prove it is inverse function. e. If you answered no for some of the above questions. For what domain and range the function has an inverse function? Prove your answer.

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