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value of the fun...
Discrete
Mathematics
and Its
Applications
Sixth Edition

Kenneth

H.

Rosen

AT&T Laboratories

Boston
Bangkok
Milan

Burr...
The

McGraw Hilt Compames

4

DISCRETE MATHEMATICS AND ITS APPLICATIONS, SIXTH EDITION
International Edition

2007

Exclus...
Contents
Preface vii

T he MathZone Companion Website xviii

To the Student xx

1

The Foundations: Logic and Proofs ........
Contents

4.5

5

5. 1
5.2
5.3
5 .4
5.5
5.6

6

6. 1
6.2
6.3
6.4

Program Correctness . . . . . . . . . . . . . . . . . . ...
Contents

v

9.5
9.6
9.7
9 .8

Euler and Hamilton Paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
About the Author
K enneth H.Laboratorieshad Monmouth County, New Jersey. He currentlythe Technical Staff
Rosen has
a long ...
Preface
I discrete mathematics. For the student, my purpose was to present material in a precise,
readable manner, with th...
vJli

Preface

3 . Discrete Structures: A course in discrete mathematics should teach students how to work
with discrete s...
Preface ix
Logic
•

Coverage of logic has been amplified with key
ideas explained in greater depth and with more
care.

•
...
x

Preface

Exercises and Examples
•

Many new routine exercises and examples have been
added throughout, especially at sp...
Preface xi
WRITING STYLE
The writing style in this book is direct and pragmatic. Precise mathe­
matical language is used w...
Iii

Preface

and techniques of that chapter. To answer these questions students need to write long answers,
rather than j...
Preface xiii
Optional Computer
Science Sections

Chapter

Core Sections

1
2
3
4
5
6
7
8
9
10
11
12

1 . 1-1 .7 (as needed...
xiv

Preface
bank containing over 1 300 exam questions to choose from. Answers to all sample tests and test
bank questions...
Preface xv
Stephanie Fitchett,
Florida Atlantic University

Jonathan Knappenberger,
LaSalle University

Henry Ricardo,
Med...
xvi

Preface

Scott Buffett,
University ofNew Brunswick

David Jonah,
Wayne State University

HoKuen Ng,
San Jose State Un...
Preface

xvii

Daniel Somerville,
University ofMassachusetts, Boston

Philip D. Tiu,
Oglethorpe University

Thomas Upson,
...
The MathZone Companion Website
MathZon�

'"
,

T he extensive companion website accompanying this text has been substantia...
The MathZone Companion Website

xix

•

Applications o Discrete Mathematics
f

•

A Guide to Proo Writing
f-

•

Common Mi...
To the Student

W

hat is discrete mathematics? Discrete mathematics is the part of mathematics devoted to
the study of di...
To the Student

xxi

percentage of the exercises require original thought. This is intentional. The material discussed
in ...
xxii

To the Student
The best approach is to try exercises yourself before you consult the answer section at the
end of th...
C H A P T E R

The Foundations :
Logic and Proofs
1.1 Propositional
Logic

1.2 Propositional
Equivalences

1.3 Predicates ...
2

1 -2

1 / The Foundations: Logic and Proofs

EXAMPLE l

Exam= �

All the following declarative sentences are propositio...
1 . 1 Propositional Logic 3

1-3

unkS �

DEFINITION 1

We now turn our attention to methods for producing new proposition...
4

1 / The Foundations: Logic and Proofs

/-4

The negation of a proposition can also be considered the result of the oper...
1 . 1 Propositional Logic

1-5

5

Here, we mean that students who have taken both calculus and computer science can take ...
6

I / The Foundations:

Logic and Proofs

1-6

TABLE 4 The Truth Table for

TABLE 5 The Truth Table for
the Conditional S...
1 . 1 Propositional Logic

/-7

7

If you manage to get a 1 00% on the final, then you would expect to receive an A. If yo...
8

I / The Foundations: Logic and Proofs

1-8

statement. In mathematical reasoning, we consider conditional statements of...
1 . 1 Propositional Logic

1-9

9

The converse is
"If the home team wins, then it is raining."
The inverse is
"If it is n...
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Discrete mathematics and it s applications (sixth edition)
Discrete mathematics and it s applications (sixth edition)
Discrete mathematics and it s applications (sixth edition)
Discrete mathematics and it s applications (sixth edition)
Discrete mathematics and it s applications (sixth edition)
Discrete mathematics and it s applications (sixth edition)
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Discrete mathematics and it s applications (sixth edition)
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Discrete mathematics and it s applications (sixth edition)
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Discrete mathematics and it s applications (sixth edition)
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Discrete mathematics and it s applications (sixth edition)
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Discrete mathematics and it s applications (sixth edition)
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