Section 5.3
24.
a) Odd integers are obtained from other odd integers by adding 2. Thus we can define this set S
as follows: 1 S ; and if n S , then n + 2 S .
b) Powers of 3 are obtained from other powers of 3 by multiplying by 3. Thus we can define this
s

Section 5.2 pages 341-344, exercises 2, 6, 9, 10, 16, 24, 30, 36, 39
2. Use strong induction to show that all dominoes fall in an infinite arrangement of dominoes if
you know that the
first three dominoes fall, and that when a domino falls, the domino thr

Section 1.6, pages 78-80, problems 24, 26, 28
24. Identify the error or errors in this argument that supposedly
shows that if x(P(x) Q(x) is true then
xP(x) xQ(x) is true.
1. x(P(x) Q(x)
Premise
2. P(c) Q(c)
Universal instantiation from (1)
3. P(c)
Simpli

COSC 2375
Spring 2015
Assignment 1
August 28, 2015
Do the following questions in the textbook from Sections 1.1, 1.2 and 1.3. Remember to keep
track of any websites, books, or other people that help you so that you can list them in your
Collaboration Stat

Section 1.1 Pg 12-16 #6,10,32,42
6. Suppose that Smartphone A has 256MB RAM and 32GB ROM, and the resolution of its camera is 8 MP;
Smartphone B has 288 MB RAM and 64 GB ROM, and the resolution of its camera is 4 MP; and Smartphone C
has 128 MB RAM and 32

Section 1.1 Pg 12-16 #6,10,32,42
6. Suppose that Smartphone A has 256MB RAM and 32GB ROM, and the resolution of its camera is 8 MP;
Smartphone B has 288 MB RAM and 64 GB ROM, and the resolution of its camera is 4 MP; and Smartphone C
has 128 MB RAM and 32

Section 3.1, pages 202-204, exercises 26, 27, 41, 42, 47, 56
26. Change Algorithm 3 so that the binary search procedure compares x to am at each stage of the algorithm, with the
algorithm terminating if x = am. What advantage does this version of the algo

COSC 2375
Spring 2015
Assignment 5
Algorithms, Chapter 3
150 Points
Due September 20
Do the following questions in the textbook from Sections 3.1, 3.2, and 3.3. Remember to keep
track of any websites, books, or other people that help you so that you can l

COSC 2375
Do the following questions in the textbook from Sections 1.1, 1.2 and 1.3. Remember to keep
track of any websites, books, or other people that help you so that you can list them in your
Collaboration Statement in the writeup with your answers. T

COSC 2375
Spring 2015
Algorithms, Chapter 3
Do the following questions in the textbook from Sections 3.1, 3.2, and 3.3. Remember to keep
track of any websites, books, or other people that help you so that you can list them in your
Collaboration Statement

Section 10.1,
11. Let G be a simple graph. Show that the relation R on the set of vertices of G such that uRv if
and only if there is an edge associated to cfw_u, v is a symmetric, irreflexive relation on G. If uRv,
then there is an edge associated with c

Week 1
Weekly Objectives: At the end of Week 1, students should be able to
1.
2.
3.
4.
5.
6.
understand the basic terminology of propositional logic, including logical connectives
show how to construct truth tables
illustrate the importance of logic with

1.4 #14, 26, 32
14. Determine the truth value of each of these statements if
the domain consists of all real numbers.
a) x(x^3 = 1) True, x=-1 is same as x^3=-1
b) x(x^4 < x^2) True
c) x(x)^2 = x^2) True, (-x^2) is the same as x^2
d) x(2x > x) False
26. T

Section 3.1, pages 202-204, exercises 2, 6, 10, 14
2. Determine which characteristics of an algorithm described in the text (after Algorithm 1) the following procedures
have and which they lack.
a) procedure double(n: positive integer)
while n > 0
n := 2n

Section 1.4, pages 53-57: problems 24, 34, 40, 46, 52
24. Translate in two ways each of these statements into logical
expressions using predicates, quantifiers, and logical
connectives. First, let the domain consist of the students
in your class and secon

Answer Key
Section 4.1
16. Assume that a b (mod m). This means that m | a b, say a b = mc, so that a = b + mc.
Now let us compute a mod m. We know that b = qm + r for some nonnegative r less than m
(namely, r = b mod m). Therefore we can write a = qm + r

Section 5.1
3.
a) 12 = 1.2.3/6
b) Both sides of P(1) shown in part (a) equal 1.
c) 12 + 22 + .+ k2 = k(k +1)(2k + 1)/6
d) For each k 1 that P(k) implies P(k + 1); in other words, that assuming the inductive
hypothesis (see part c) we can show 12 + 22 + .+

SOLUTION
Section 5.2
2. Let P(n) be the statement that the nth domino falls. We want to prove that P(n) is true for all
positive integers n. For the basis step we note that the given conditions tell us that P(1), P(2),
and P(3) are true. For the inductive

Solution Key for October 23 and 24 Assignment
2 Solution
We need to show that 13 937 1 (mod 2436), or in other words, that 13 937 1 = 12180 is divisible by
2436. A calculator shows that it is, since 12180 = 2436 5.
6 Solution
a) The first step of the proc

Discrete Structures (COSC2375),
Part 3 of Lecture 1 (Sections
1.6, 1.7, and 1.8 of Chapter 1
LawrenceSeventh
Osborne
of [Rosen;
Edition])
09/11/16
COSC-2375, Lecture 1, Part 3
1
Overview of Chapter 1 [Rosen;
Seventh
Edition]
Propositional Logic
The Langua

Discrete Structures (COSC2375),
Part 2 of Lecture 1 (Sections
1.4 and 1.5 of Chapter 1 of
Lawrence
Osborne Edition])
[Rosen;
Seventh
09/11/16
COSC-2375, Lecture 1, Part 2
1
Overview of Chapter 1 [Rosen;
Seventh Edition]
Propositional Logic
The Language of

Discrete Structures (COSC2375),
Lecture 3 Algorithms
(Chapter 3 of [Rosen;
Lawrence
Osborne
Seventh
Edition])
09/11/16
COSC-2375, Lecture 3
1
Overview of last lecture
Basic Structures
Sets
The Language of Sets
Set Operations
Set Identities
Functions
09/11

Discrete Structures (COSC2375),
Lecture 2 (Chapter 2 of
[Rosen; Seventh Edition])
Lawrence Osborne
09/11/16
COSC-2375, Lecture 2
1
Overview of last lecture
Propositional Logic
The Language of
Propositions
Applications
Logical Equivalences
Proofs
Rules of

Discrete Structures (COSC2375),
Lecture 1 Part 1 (Sections 1.1,
1.2, and 1.3 of Chapter 1 of
Lawrence
Osborne Edition])
[Rosen;
Seventh
09/11/16
COSC-2375, Lecture 1, Part 1
1
Discrete Structures
COSC-2375 is a 3 semester credit hour course.
Grading is as

Week 2
Weekly Objectives: At the end of Week 2, students should be able to
1. describe and discuss predicate logic, especially existential and universal quantification
2. explain how to translate between English sentences (or mathematical statements) and