Test Total
Name
Test 3 Introduction to Discrete Mathematics 3450:208
June 27, 2008
Show your work.
Dr. Norfolk
1. (a) Use the Principle of Mathematical Induction to prove that
3 + 5 + 7 + + (2n + 1) = n(n + 2), for n 1
10 points
(b) Let P (n) be a predica
Test Total
Name
Test 3 Introduction to Discrete Mathematics 3450:208 Dr. Norfolk
Friday, August 5th, 2005
Show your work.
1. Mark each of the following statements True or False, as appropriate:
(a) cfw_a, b
(b) cfw_a, b
(c) |cfw_a, cfw_b, c| = 2
(d) If A,
Test Total
Name
Test 1
Introduction to Discrete Mathematics 3450:208
June 2, 2008
Show your work.
Dr. Norfolk
1. Consider the conditional E = p q r.
Use de Morgans laws to write simplied versions of the following :
The negation of E :
5 points
The inver
Test Total
Name
Test 2 Introduction to Discrete Mathematics 3450:208 Dr. Norfolk
July 30th, 2007
Show your work.
1. Consider the statement Addition of natural numbers is commutative.
(a) Write this statement as a symbolic statement with quantiers.
5 point
Test Total
Name
Test 3 Introduction to Discrete Mathematics 3450:208 Dr. Norfolk
Wednesday, August 8th, 2007
Show your work.
1. Mark each of the following statements True or False, as appropriate:
(a) cfw_x I : 0 < x < 4 = cfw_1, 2, 3
R
(b) b cfw_a, cfw_b
Test Total
Name
Test 2 Introduction to Discrete Mathematics 3450:208 Dr. Norfolk
November 3rd, 2004
Show your work.
1. Consider the statement The integers are closed under division.
(a) Write this statement as a symbolic statement with quantiers.
5 points
Test Total
Name
Test 3 Introduction to Discrete Mathematics 3450:208
June 27, 2008
Show your work.
Dr. Norfolk
1. (a) Use the Principle of Mathematical Induction to prove that
3 + 5 + 7 + + (2n + 1) = n(n + 2), for n 1
10 points
(b) Let P (n) be a predica
Test Total
Name
Test 1
September 29th, 2004
Show your work.
Introduction to Discrete Mathematics 3450:208
Dr. Norfolk
1. Consider the conditional E = p q r.
Use de Morgans laws to write simplied versions of the following :
The negation of E :
5 points
T
Test Total
Name
Test 2 Introduction to Discrete Mathematics 3450:208 Dr. Norfolk
July 21st, 2006
Show your work.
1. Consider the statement Multiplication of integers is commutative.
(a) Write this statement as a symbolic statement with quantiers.
5 points
Test Total
Name
Test 1
Introduction to Discrete Mathematics 3450:208
July 11th, 2007
Show your work.
Dr. Norfolk
1. Consider the conditional E = p q r.
Use de Morgans laws to write simplied versions of the following :
The negation of E :
5 points
The in
Test Total
Name
Test 1
Introduction to Discrete Mathematics 3450:208 Dr. Norfolk
July 6th, 2005
Show your work.
1. Consider the conditional E = p q r.
Use de Morgans laws to write simplied versions of the following :
The negation of E :
5 points
The inv
Test Total
Name
Test 3 Introduction to Discrete Mathematics 3450:208 Dr. Norfolk
Monday, November 29th, 2004
Show your work.
1. Mark each of the following statements True or False, as appropriate:
(a) cfw_a cfw_a, b
(b) cfw_a cfw_a, b
(c) If A, B are sets
Test Total
Name
Test 2 Introduction to Discrete Mathematics 3450:208
June 13, 2008
Show your work.
Dr. Norfolk
1. Consider the statement Every non-zero rational number has a reciprocal which is rational.
(a) Write this statement as a symbolic statement wi
Test Total
Name
Test 2 Introduction to Discrete Mathematics 3450:208 Dr. Norfolk
July 25th, 2005
Show your work.
1. Consider the statement Addition of integers is commutative.
(a) Write this statement as a symbolic statement with quantiers.
5 points
(b) W
Test Total
Name
Test 3 Introduction to Discrete Mathematics 3450:208 Dr. Norfolk
Friday, August 4th, 2006
Show your work.
1. Mark each of the following statements True or False, as appropriate:
(a) cfw_a, b
(b) cfw_a, b
(c) |cfw_a, cfw_b, c| = 2
(d) If A,
Test Total
Name
Test 2 Introduction to Discrete Mathematics 3450:208 Dr. Norfolk
July 21st, 2006
Show your work.
1. Consider the statement Multiplication of integers is commutative.
(a) Write this statement as a symbolic statement with quantiers.
5 points
Test Total
Name
Test 2 Introduction to Discrete Mathematics 3450:208 Dr. Norfolk
July 25th, 2005
Show your work.
1. Consider the statement Addition of integers is commutative.
(a) Write this statement as a symbolic statement with quantiers.
5 points
(b) W
Test Total
Name
Test 3 Introduction to Discrete Mathematics 3450:208 Dr. Norfolk
Wednesday, August 8th, 2007
Show your work.
1. Mark each of the following statements True or False, as appropriate:
(a) cfw_x I : 0 < x < 4 = cfw_1, 2, 3
R
(b) b cfw_a, cfw_b
Test Total
Name
Test 3 Introduction to Discrete Mathematics 3450:208 Dr. Norfolk
Friday, August 4th, 2006
Show your work.
1. Mark each of the following statements True or False, as appropriate:
(a) cfw_a, b
(b) cfw_a, b
(c) |cfw_a, cfw_b, c| = 2
(d) If A,
Test Total
Name
Test 4 Introduction to Discrete Mathematics 3450:208 Dr. Norfolk
Friday, August 12th, 2005
Show your work.
1. For any real number x, and any positive integer n, dene f (x, n) = xn , so f (2, 3) = 23 =
8, f (0.5, 2) = 0.52 = 0.25.
(a) Write
Test Total
Name
Test 4 Introduction to Discrete Mathematics 3450:208 Dr. Norfolk
Friday, August 11th, 2006
Show your work.
x
1. For any real number x, and any positive integer n, dene f (x, n) =
, so
n
2.0
4.5
f (2.0, 3) =
= 0, f (4.5, 2) =
= 3.
3
2
(a) W
Test Total
Name
Test 4 Introduction to Discrete Mathematics 3450:208
July 11, 2008
Show your work.
Dr. Norfolk
1. Tims Treadmills started manufacturing in the year 2000. Each of their products carries a
10-character code, as follows:
The rst 2 characters
Test Total
Name
Test 4 Introduction to Discrete Mathematics 3450:208 Dr. Norfolk
Friday, August 17th, 2007
Show your work.
1. For any real number x, and any positive integer n, dene f (x, n) = xn , so that
f (2.0, 3) = (2.0)3 = 8, f (1.5, 2) = (1.5)2 = 3.
Test Total
Name
Test 3 Introduction to Discrete Mathematics 3450:208 Dr. Norfolk
Friday, August 5th, 2005
Show your work.
1. Mark each of the following statements True or False, as appropriate:
(a) cfw_a, b
(b) cfw_a, b
(c) |cfw_a, cfw_b, c| = 2
(d) If A,
Test Total
Name
Test 2 Introduction to Discrete Mathematics 3450:208
June 13, 2008
Show your work.
Dr. Norfolk
1. Consider the statement Every non-zero rational number has a reciprocal which is rational.
(a) Write this statement as a symbolic statement wi
Test Total
Name
Test 1
Introduction to Discrete Mathematics 3450:208 Dr. Norfolk
July 5th, 2006
Show your work.
1. Consider the conditional E = p q r.
Use de Morgans laws to write simplied versions of the following :
The negation of E :
5 points
The inv
Test Total
Name
Test 1
Introduction to Discrete Mathematics 3450:208 Dr. Norfolk
July 6th, 2005
Show your work.
1. Consider the conditional E = p q r.
Use de Morgans laws to write simplied versions of the following :
The negation of E :
5 points
The inv
Test Total
Name
Test 1
Introduction to Discrete Mathematics 3450:208
July 11th, 2007
Show your work.
Dr. Norfolk
1. Consider the conditional E = p q r.
Use de Morgans laws to write simplied versions of the following :
The negation of E :
5 points
The in
Test Total
Name
Test 1
Introduction to Discrete Mathematics 3450:208
June 2, 2008
Show your work.
Dr. Norfolk
1. Consider the conditional E = p q r.
Use de Morgans laws to write simplied versions of the following :
The negation of E :
5 points
The inver
Test Total
Name
Test 2 Introduction to Discrete Mathematics 3450:208 Dr. Norfolk
July 30th, 2007
Show your work.
1. Consider the statement Addition of natural numbers is commutative.
(a) Write this statement as a symbolic statement with quantiers.
5 point