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MA134A
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EXAM 3
Grade:
April 2012
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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 follows:
x, y, A, xRy 4 | (x y ).
1. Prove that R is a
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 involving P would be done in two steps:
1. Basis step:
MA 134 EXAM #4
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Dec. 7, 2015
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closed book, closed notes, no electronic access
Answer all questions
(15 pts.) 1. Define:
a) a function f from a set X to a set
MA 134 EXAM #1
Sept. 30, 2015
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Answer all questions
(15 points) 1. Define:
a) a RELATION G from a set A to a
MA 134 EXAM #3
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Oct. 31, 2014
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Answer all questions
(40 pts.) 1. Use Mathematical Induction to prove the following statement:
For all integers n 1, 2 + 4 + 6
MA 134 EXAM #1
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Sept. 26, 2014
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Answer all questions
(15 pts.) 1. Define:
The Cartesian Product (AB) of two sets A and B
A relation R from a set A to a set B
MA 134 EXAM #2
March 13, 2015
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Answer all questions
(10 points) 1. Write the negation of
a) x, if P(x) then
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 you
are, just check the errata document as you read th
MA 134 EXAM #1
Feb. 18, 2015
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Answer all questions
(10 points) 1. Use DeMorgans Laws to write the negations
MA 134 EXAM #3
Nov. 11, 2015
closed book, closed notes, no electronic access
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Answer all questions
(25 pts.) 1. Use Mathematical Induction to prove the foll
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. The proof is by contradiction: suppose that its not the
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 non-empty, and thus (by the well-ordering principle) has
Name:
MA134A
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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, explain.
1. f : Q cfw_5
r
2. f : Z
Q
r
5r
N
n | n| + 2
3.
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MA134A
EXAM 1
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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]
Grade:
February 2012
2 (12pts) Use a truth table to che
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MA134
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FINAL EXAM
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1. (8pts)
Use a truth table to determine if the following is a tautology. Explain.
[r (p q )] [(r p) (r q )]
Grade:
May 2012
2 (10pts) Let U = Z . Are the follow
MA 134 EXAM #2
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Oct. 28, 2015
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Answer all questions
(15 pts.) 1. Define each of the following with a universal conditional statement:
a) x, r(x) is a suffici