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15. Every function is a relation. A. True B. False 16. Mathematical Induction technique can be stated as: (P(1)k(P(k)P(k+1)))nP(n) A. True B. False 17. The following equation is a representation of the sum rule in set theory. 18. (ab)4 is a binomial expression A. True B. False 19. Probability of an event that will never happen is 0 A. True B. False 20. For an unbiased dice, the probability that the outcome of throwing the dice twice is (5,5) equals 1/25. A. True B. False 21. Performance of an experiment with two possible outcomes is called a Bernoulli trial. A. True B. False 22. A dice is biased so that the number 5 appears twice as often as each other number. What is the probabilities that the outcome is 3 ? A. 1/6 B. 2/6 C.1/7D.2/7 23. Let X be a random variable equal to the sum of the numbers that appear when two fair dice are rolled. What is the expected value of X ? A. 3.5 B. 7 C. 5 D. 4.5 24. For an unbiased coin, what is the probability of exactly two heads to come up when the coin is tossed four times? A. 3/16 B. 1/4 C. 3/8 D. 1/8 25. The adjacency matrix for Cn has 1's. A. 2n B. n C. n2 D. n(n1) 26. A proof by mathematical induction has two parts namely and A. simple step, complex step B. P(n) step, P(n+1) step C. basis step, inductive step D. P(k) step, P(k+1) step 77. If T is a binary tree with 100 vertices, its minimum height is A. 6 B. 7 C. 8 D. 9 8. Wn has edges and vertices. A. 4n,n+1 B. 2n,n C. 4n,n D. 2n,n+1 In a multigraph, for an edge {u,v},u=v A. True B. False A loop at a vertex adds 1 to the degree of that vertex. A. True B. False