Name:
MA134A
SSN:
EXAM 3
Grade:
April 2012
I pledge my honor that I have abided by the Stevens Honor System.
1 (16pts)
Let A = cfw_5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7. Let R be the relation dened as
Appendix - Methods of proof
Induction
Definition 1. Induction is a way of proving universal statements over natural
numbers. Let P (x) be a predicate over the natural numbers. An argument by
induction
MA 134 EXAM #4
Name (please print):_
Dec. 7, 2015
I pledge my honor that I have abided by the Stevens Honor System
signature: _
closed book, closed notes, no electronic access
Answer all questions
(15
MA 134 EXAM #1
Sept. 30, 2015
closed book, closed notes, no electronic access
Name (please print):_
I pledge my honor that I have abided by the Stevens Honor System
signature: _
Answer all questions
(
MA 134 EXAM #3
Name (please print):_
Oct. 31, 2014
I pledge my honor that I have abided by the Stevens Honor System
signature: _
Answer all questions
(40 pts.) 1. Use Mathematical Induction to prove t
MA 134 EXAM #1
Name (please print):_
Sept. 26, 2014
I pledge my honor that I have abided by the Stevens Honor System
signature: _
Answer all questions
(15 pts.) 1. Define:
The Cartesian Product (AB) o
MA 134 EXAM #2
March 13, 2015
closed book, closed notes, no electronic access
Name (please print):_
I pledge my honor that I have abided by the Stevens Honor System
signature: _
Answer all questions
(
HW #1
Under General Information on our CANVAS page I have posted a copy of the Textbook errata.please
transfer those to your textbook if you are using a pdf version of the text, as some of you told me
MA 134 EXAM #1
Feb. 18, 2015
closed book, closed notes, no electronic access
Name (please print):_
I pledge my honor that I have abided by the Stevens Honor System
signature: _
Answer all questions
(1
MA 134 EXAM #3
Nov. 11, 2015
closed book, closed notes, no electronic access
Name (please print):_
I pledge my honor that I have abided by the Stevens Honor System
signature: _
Answer all questions
(2
Theorem (Principle of Mathematical Induction).
Let Sn be a statement about n N. If (1) S1 is true, and (2) For each n N, the truth of Sn implies the
truth of Sn+1, then Sn is true for all n N. Proof.
Lemma.
Every integer greater than 1 has at least one prime divisor.
Proof.
(By contradiction) Assume there is some integer greater than 1 with no prime divisors. Then the set of all
such integers is n
Name:
MA134A
SSN:
Grade:
EXAM 2
March 2012
I pledge my honor that I have abided by the Stevens Honor System.
1 (12pts)
1. Are the following functions injections (1-1)? surjections (onto)? If not, expl
Name:
SSN:
MA134A
EXAM 1
I pledge my honor that I have abided by the Stevens Honor System.
1 (15pts)
True or false? If false, explain.
Let U = Z .
1. y !x [xy = 0]
2. x y [3x 2y = 10]
3. y x [xy = x]
Name:
MA134
SSN:
FINAL EXAM
I pledge my honor that I have abided by the Stevens Honor System.
1. (8pts)
Use a truth table to determine if the following is a tautology. Explain.
[r (p q )] [(r p) (r q
MA 134 EXAM #2
Name (please print):_
Oct. 28, 2015
I pledge my honor that I have abided by the Stevens Honor System
signature: _
Answer all questions
(15 pts.) 1. Define each of the following with a u