advertisement

Questions 1. True or false The following set of numbers are pairwise relatively prime - 17, 18, 19, 23 Answer: true 2. Find the prime factorization of the composite number: 252 (If the base number does not belong to the prime factorization then just put 0 in for the blank). 2 raised to the power of 3 raised to the power of 5 raised to the power of 7 raised to the power of 2 2 0 1 3. Suppose you want to use mathematical induction to prove that: 12+22+…+n2= n(n+1)(2n+1) /6 for all positive integers. To show P(k) implies P(k+1) you assume the equality in the statement P(k) and-a. Add (k+1)2 to both sides. b. Add k2+1 to both sides. c. Add k+1 to both sides. d. Add k to both sides. 4. Find f(3) if f(n) = f(n-1)/f(n-2), f(0)=2, f(1) =5. a. 5/2 b. 1/2 c. 3/2 d. 1 5. Find the best big-oh function for the function: f (n) = a. 1 b. N c. n^2 d. n^3 6. For which of the following is the recursively defined set S equal to {a, 2a, 3a, 4a, 5a, ...}? a. b. c. d. this is the right one ( a in S, x in S then a+x in S) (4th option is right) 7. True or false: If 1 < 0, then 3 = 4. Answer: True 8. Baskin-Robbins offers 31 different flavors of ice cream. One of their items is a bowl consisting of three scoops of ice cream, each a different flavor. How many such bowls are possible? Answer: 4495 9. True or False (p → q) ∧ (¬p → q) ≡ q. Answer: true