Mathematics 2513-001
Name (please print)
Examination III Form A
April 27, 2006
Instructions: Give brief, clear answers. Prove means give an argument.
I.
(4)
II.
(4)
III.
(4)
IV.
(4)
V.
(4)
VI.
(5)
VII.
(5)
Let f : X Y and g : Y Z. Prove that if f and g ar
MATH 2513-001
Discrete Mathematics
Fall 2009
Finite Sets, Innite Sets and Cardinality
1. Intuition. Discuss intuition about nite sets.
2. Denition. For n Z+ , dene n to be the set of positive integers which are less than or equal to
n:
n = cfw_m Z+ | m n
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MATH 2513-001
Discrete Mathematics
Fall 2009
Symmetries of the plane, rigid motions
1. The euclidean plane E2 is just the usual cartesian plane R2 = R R with some euclidean geometry
added in to the mix. This is commonly done by using Pythagoras Theorem to
Mathematics 2513-001
Name (please print)
Examination I Form A
February 14, 2006
Instructions: Give brief, clear answers.
I.
(2)
II.
(3)
III.
(4)
IV.
(9)
Write the following as an implication: a2 2 for at most one a.
Using step-by-step logic, simplify the
Mathematics 2513-001
Name (please print)
Examination II Form B
March 23, 2006
Instructions: Give brief, clear answers. Prove means give an argument. In giving denitions, give the precise
denition, using logical notation and/or set notation as appropriate.
Mathematics 2513-001
Name (please print)
Examination II Form B
March 23, 2006
Instructions: Give brief, clear answers. Prove means give an argument. In giving denitions, give the precise
denition, using logical notation and/or set notation as appropriate.
Math 2513 homework
28. (4/13) 2.4 # 28, 30, 38-40
29. (4/13) Prove the following.
(a) a Z, a a mod m.
(b) a Z, b Z, a b mod m b a mod m.
(c) a Z, b Z, c Z, (a b mod m b c mod m) a c mod m.
30. (4/13) Let p be prime.
(a) Prove that gcd(a, p) = 1 if and onl
Mathematics 2513-001
Name (please print)
Final Examination Form A
May 9, 2006
Instructions: Give brief, clear answers. Prove means give an argument.
I.
(5)
Let T (s, c) be Student s has taken course c. Write each of the following statements in logical not
Mathematics 2513-001
Name (please print)
Final Examination Form B
May 9, 2006
Instructions: Give brief, clear answers. Prove means give an argument.
I.
(4)
Use proof by contradiction to prove that the sum of a rational number and an irrational number must
Mathematics 2513-001
Name (please print)
Examination III Form B
April 27, 2006
Instructions: Give brief, clear answers. Prove means give an argument.
I.
(4)
II.
(4)
III.
(4)
IV.
(4)
V.
(5)
VI.
(4)
VII.
(5)
Let f : X Y and g : Y Z. Prove that if f and g ar
Mathematics 2513-001
Name (please print)
Examination II Form A
March 23, 2006
Instructions: Give brief, clear answers. Prove means give an argument. In giving denitions, give the precise
denition, using logical notation and/or set notation as appropriate.
Mathematics 2513-001
Name (please print)
Examination I Form B
February 14, 2006
Instructions: Give brief, clear answers.
I.
(3)
Using step-by-step logic, simplify the following expression: (Q z, ( R(z) P (z) )
(Q z, ( R(z) P (z) ) Q z, ( R(z) P (z) )
Q z
Mathematics 2513-001
Name (please print)
Examination I Form A
February 14, 2006
Instructions: Give brief, clear answers.
I.
(2)
Write the following as an implication: a2 2 for at most one a.
II.
(3)
Using step-by-step logic, simplify the following express
Mathematics 2513-001
Name (please print)
Examination II Form A
March 23, 2006
Instructions: Give brief, clear answers. Prove means give an argument. In giving denitions, give the precise
denition, using logical notation and/or set notation as appropriate.
Mathematics 2513-001
Name (please print)
Examination I Form B
February 14, 2006
Instructions: Give brief, clear answers.
I.
(3)
II.
(2)
III.
(4)
IV.
(3)
Using step-by-step logic, simplify the following expression: (Q z, ( R(z) P (z) )
V.
(3)
Write the fol
Q1]. . . [10 points] Complete the truth table for the proposition below. The extra columns are there for
you to use to compute truth values of intermediate aggressions (if you Wish). Q2]. . . [10 points] Find a disjunctive normal form expression (involvin
MATH 2513-001
QUIZ IV
NAME: SOLUTIONS
Thursday, November 19, 2009
Q1]. . . Dene what it means for a set A to be countable.
A set A is said to be countable if A is nite or if there exists a bijection Z A.
Dene what it means for two sets A and B to have the
Fa05: MATH 2513001
Discrete Mathematics
Mmonday 09/26/2005
Midterm I
Student ID:
Name:
Instructions.
1. Attempt all questions.
2. Do not write on back of exam sheets. Extra paper is available if you need it.
3. Show all the steps of your work clearly.
Que
Fa09: MATH 2513001
Discrete Mathematics
Tuesday 11/24/2009
Midterm III
Noel Brady
9:00am10:15am
Student ID:
Name:
Instructions.
1. Attempt all questions.
2. Do not write on back of exam sheets. Extra paper is available if you need it.
3. Show all the step