Circle TAs name: H. Sahni, M. Mills, V. Coxall
Name :
Math 2602(G). Quiz 10.
April 18, 2013.
1. (1 point) How many edges are there in a graph with degree sequence 5, 4, 3, 3, 3, 2, 2?
Using the Hand-shaking theorem, we have
|E | =
1
1
deg(v ) = (5 + 4 + 3
Math 2602(G). Exam 2 Solution.
March 7, 2013
1. (2 points each) Determine whether the following statements are True for False.
(a) False There exists a suciently large k such that x is O(log x)k ).
(b) True log(x5 ) is O(log(x).
(c) True If f1 is O(g1 ) a
Circle TAs name: H. Sahni, M. Mills, V. Coxall
Name :
Math 2602(G). Exam 3.
April 11, 2013.
1. Short answers. (3 points each)
(a) How many dierent strings can be made with the letters in GATTACA?
7!
3! 2!
(b) How many strings of 7 letters (A-Z) contain ex
Circle TAs name: H. Sahni, M. Mills, V. Coxall
Name :
Math 2602(G). Quiz 1.
January 17, 2012.
1. (1 pt) Use truth tables to show that
(p q ) p q.
p
T
T
F
F
q
T
F
T
F
(1)
(p q ) p q
F
F
T
T
F
F
F
F
Since (p q ) and p q agree for all possible combinations o
Name :
Circle TAs name: H. Sahni, M. Mills, V. Coxall
Math 2602(G). Quiz 2.
January 24, 2012.
1. Use predicates, quantiers, logical connectives, and mathematical operators to express
the statement that every positive integer is the sum of squares of three
Name :
Circle TAs name: H. Sahni, M. Mills, V. Coxall
Math 2602(G). Quiz 3.
January 31, 2012.
Prove or disprove the following statements using only the denitions of even/odd
integers. For example, do not use statements such as the sum of two odd numbers i
Math 2602(G). Quiz 4 Solution.
February 14, 2012.
1. (3 points) Use the denition of big-O to prove that (x sin x + 1)2 is O(x2 ).
Let c = 4 and k = 1. Then for x > k , we have 1 x2 and x x2 . Moreover,
| sin x| 1 for any x. Using these together with the t
Name :
Circle TAs name: H. Sahni, M. Mills, V. Coxall
Math 2602(G). Quiz 5.
February 21, 2013.
For n 1, let f (n) be the sum of the n smallest positive odd integers.
1. (1 point) Find a formula for f (n) by examining the rst few values of f (n).
f (n) = n
Circle TAs name: H. Sahni, M. Mills, V. Coxall
Name :
Math 2602(G). Quiz 6 solution.
February 28, 2013.
1. (1 points) Fill in the blanks in the following recursive algorithm for computing the
number 3n for integers n 0.
procedure power(n: nonnegative inte
Math 2602(G). Quiz 7 Solution.
March 14, 2013.
1. How many strings of six letters are there
(a) if letters can be repeated? (There are 26 letters from A to Z.)
266
(b) if letters can be repeated and exactly two of the letters must be vowels (A,E,I,O,U)?
6
Circle TAs name: H. Sahni, M. Mills, V. Coxall
Name :
Math 2602(G). Quiz 8.
March 28, 2013.
(1 point each)
1. A grocery store sells 20 dierent kinds of fruits. How many ways are there to buy 5
pieces of fruits? (Fruits of the same kind are indistinguishab
Name :
Circle TAs name: H. Sahni, M. Mills, V. Coxall
Math 2602(G). Quiz 9.
April 4, 2013.
1. (3 points) Solve the recurrence relation together with the intition condition given
an = 4an1 + 5an2 for n 2, a0 = 7, a1 = 5.
The solutions of r2 + 4 r 5 = 0 are
Math 2602(G). Exam 1 Solution.
February 7, 2012.
1. (9 points) Fill in the values in the truth table.
p
q
(p q ) (p q ) p (p q ) (p q ) q
T
T
T
F
T
T
F
F
T
F
F
T
F
T
T
F
F
T
T
T
2. (9 points) Determine the truth value of each of the following statements.