science, but not both, can enroll in this
class. Here, we mean that students who
have taken both calculus and a computer
science course cannot take the class. Only
those who have taken exactly one of the
two courses can take the class. Similarly,
when a m

relationships between finite (or
countable) sets are studied, and when
processes involving a finite number of
steps are analyzed. A key reason for the
growth in the importance of discrete
mathematics is that information is stored
and manipulated by comput

was resourceful obtaining images for the
new biographical footnotes. The accuracy
and quality of this new edition owe much
to Jerry Grossman and Jean-Claude Evard,
who checked the entire manuscript for
technical accuracy and Georgia Mederer,
who checked t

and q. The conjunction p q is true
when both p and q are true and is false
otherwise. Table 2 displays the truth table
of p q. This table has a row for each of
the four possible combinations of truth
values of p and q. The four rows
correspond to the pair

course she took! Math courses based on
the material studied in discrete
mathematics include logic, set theory,
number theory, linear algebra, abstract
algebra, combinatorics, graph theory, and
probability theory (the discrete part of
the subject). Also, d

successfully apply these tools using your
own creativity. One of the primary goals of
this course is to learn how to attack
problems that may be somewhat different
from any you may have previously seen.
Unfortunately, learning how to solve only
particular

although the conditional operator has
precedence over the biconditional
operator. Table 8 displays the precedence
levels of the logical operators, , , , ,
and . Logic and Bit Operations
Computers represent information using
bits. A bit is a symbol with tw

companion website immediately
preceding this To the Student message.
P1: 1/1 P2: 1/2 QC: 1/1 T1: 2 FRONT-7T
Rosen-2311T MHIA017-Rosen-v5.cls May
13, 2011 10:21 xx To the Student TABLE 1
Hand-Icon Exercises and Where They Are
Used Section Exercise Section

When execution of a program encounters
such a statement, S is executed if p is true,
but S is not executed if p is false, as
illustrated in Example 8. EXAMPLE 8
What is the value of the variable x after
the statement if 2 + 2 = 4 then x := x + 1 if
x = 0

student backgrounds and ability levels.
Teaching Suggestions This guide contains
detailed teaching suggestions for
instructors, including chapter overviews
for the entire text, detailed remarks on
each section, and comments on the
exercise sets. Printable

University, San Marcos David Snyder
Texas State University, San Marcos Wasin
So San Jose State University Bogdan
Suceava California State University,
Fullerton Christopher Swanson Ashland
University Bon Sy Queens College
Matthew Walsh Indiana-Purdue
Unive

EXERCISE SETS Each chapter is followed
by a rich and varied set of supplementary
exercises. These exercises are generally
more difficult than those in the exercise
sets following the sections. The
supplementary exercises reinforce the
concepts of the chap

conditional statement The home team
wins whenever it is raining? Solution:
Because q whenever p is one of the ways
to express the conditional statement p
q, the original statement can be rewritten
as If it is raining, then the home team
wins. Consequentl

book and provided me with their valuable
feedback and helpful suggestions. Their
input has made this a much better book
than it would have been otherwise. I
especially want to thank Jerrold
Grossman, Jean-Claude Evard, and
Georgia Mederer for their techni

projects found at the end of each chapter
are also included in this volume. Also
included are a guide to writing proofs and
an extensive description of common P1:
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has been taken to balance the mix of
notation and words in mathematical
statements. MATHEMATICAL RIGOR AND
PRECISION All definitions and theorems
in this text are stated extremely carefully
so that students will appreciate the
precision of language and ri

Applets These applets enable you to
interactively explore how important
algorithms work, and are tied directly to
material in the text with linkages to
examples and exercises. Additional
resources are provided on how to use and
apply these applets. Self A

website for this book found at
www.mhhe.com/rosen. You will find
many Extra Examples designed to clarify
key concepts; Self Assessments for
gauging how well you understand core
topics; Interactive Demonstration Applets
exploring key algorithms and other
c

exercise An extremely challenging
exercise An exercise containing a result
used in the book (Table 1 on the following
page shows where these exercises are
used.) (Requires calculus) An exercise
whose solution requires the use of limits
or concepts from di

develop an arsenal of different proof
methods that will enable us to prove
many different types of results. After
introducing many different methods of
proof, we will introduce several strategies
for constructing proofs. We will introduce
the notion of a

at least 32GB of memory and express this
in simple English. Solution: The negation
is It is not the case that Vandanas
smartphone has at least 32GB of
memory. This negation can also be
expressed as Vandanas smartphone does
not have at least 32GB of memory

intermediate exercises, and many
challenging exercises. Exercises are stated
clearly and unambiguously, and all are
carefully graded for level of difficulty.
Exercise sets contain special discussions
that develop new concepts not covered in
the text, enab

computations in discrete mathematics,
examples, and exercises that can be
worked using this computer algebra
system. Two versions, Exploring Discrete
Mathematics with MapleTM and
Exploring Discrete Mathematics with
MathematicaTM will be available.
Applica

Rosen-2311T MHIA017-Rosen-v5.cls May
13, 2011 10:21 The Companion Website
The extensive companion website
accompanying this text has been
substantially enhanced for the seventh
edition This website is accessible at
www.mhhe.com/rosen. The homepage
shows t

Hammond Herbert Enderton University of
California, Los Angeles Anthony Evans
Wright State University Kim Factor
Marquette University Margaret Fleck
University of Illinois, Champaign Peter
Gillespie Fayetteville State University
Johannes Hattingh Georgia S

be combined. DEFINITION 5 Let p and q
be propositions. The conditional
statement p q is the proposition if p,
then q. The conditional statement p q
is false when p is true and q is false, and
true otherwise. In the conditional
statement p q, p is called t

tend to make.You are encouraged to
review this list from time to time to help
avoid these common traps. (Also available
in the Students Solutions Guide.) Advice
onWriting Projects This guide offers
helpful hints and suggestions for the
Writing Projects in

ARISTOTLE (384 b.c.e.322 b.c.e.)
Aristotle was born in Stagirus (Stagira) in
northern Greece. His father was the
personal physician of the King of
Macedonia. Because his father died when
Aristotle was young, Aristotle could not
follow the custom of follow

pledge many politicians make when
running for office is If I am elected, then I
will lower taxes. P1: 1/1 P2: 1/2 QC: 1/1
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Propositional Logic 7 If the politician is
elected, voters would