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