501 8.1 Applications of Recurrence Relations. 445 7.1 An Introduction to Discrete Probability. 423 6.6 Generating Permutations and Combinations. 415 6.5 Generalized Permutations and Combinations. 407 6.4 Binomial Coefficients and Identities.
333 5.3 Recursive Definitions and Structural Induction. 311 5.2 Strong Induction and Well-Ordering. 245 4.3 Primes and Greatest Common Divisors. 237 4.2 Integer Representations and Algorithms. 237 4.1 Divisibility and Modular Arithmetic. 109 2 Basic Structures: Sets, Functions, Sequences, Sums, and Matrices. 1 1.2 Applications of Propositional Logic. P1: 1/1 P2: 1/2 QC: 1/1 T1: 2 FRONT-7T Rosen-2311T MHIA017-Rosen-v5.cls 10:21 Contents About the Author vi Preface vii The Companion Website xvi To the Student xvii 1 The Foundations: Logic and Proofs. Discrete mathematics and its applications / Kenneth H. Library of Congress Cataloging-in-Publication Data Rosen, Kenneth H. Donnelley All credits appearing on this page or at the end of the book are considered to be an extension of the copyright page. Typeface: 10.5/12 Times Roman Printer: R.R. Burger Media Project Manager: Tammy Juran Production Services/Compositor: RPK Editorial Services/PreTeX, Inc. Louis, Missouri Lead Photo Research Coordinator: Carrie K. Cover Art © Jasper Johns/Licensed by VAGA, New York, NY Cover Designer: Studio Montage, St. Oil on Canvas (72 × 126 1/4 inches) Collection of the artist.
Rolwes Cover painting: Jasper Johns, Between the Clock and the Bed, 1981. Reed Buyer: Sandy Ludovissy Design Coordinator: Brenda A. Buczek/Rose Kernan Se nior Marketing Manager: Curt Reynolds Project Manager: Robin A. 1234567890DOW/DOW10987654321 ISBN 978-0 -07-338309 -5 MHID 0-07-338309 -0 Vice President & Editor-in-Chief: Marty Lange Editorial Director: Michael Lange Global Publisher: Raghothaman Srinivasan Executive Editor: Bill Stenquist Development Editors: Lorraine K. Some ancillaries, including electronic and print components, may not be available to customers outside the United States. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. Copyright © 2012 by The McGraw-Hill Companies, Inc. P1: 1/1 P2: 1/2 QC: 1/1 T1: 2 FRONT-7T Rosen-2311T MHIA017-Rosen-v5.cls 10:21 DISCRETE MATHEMATICS AND ITS APPLICATIONS, SEVENTH EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. Rosen Monmouth University (and formerly AT&T Laboratories) i P1: 1/1 P2: 1/2 QC: 1/1 T1: 2 FRONT-7T Rosen-2311T MHIA017-Rosen-v5.cls 10:21 Discrete Mathematics and Its Applications Seventh Edition Kenneth H. Rosen Rosen SEVENTH EDITION SEVENTH EDITION Discrete Mathematics and Its Applications DiscreteMathematicsandItsApplicationsMDDALIM114521CYANMAGYELOBLACK Key benefits of this edition are: TM Discrete Mathematics and Its Applications Kenneth H. It also reflects the insights of the author based on his experience in industry and academia. This new edition reflects extensive feedback from instructors, students, and more than 50 reviewers.
The Leading Text in Discrete Mathematics The seventh edition of Kenneth Rosen’s Discrete Mathematics and Its Applications is a substantial revision of the most widely used textbook in its field.