HAESE MATHEMATICS Specialists in mathematics publishing Mathematics for the international student Mathematics HL (Option): Discrete Mathematics HL Topic 10 FM Topic 6 Catherine Quinn Peter Blythe Chris Sangwin Robert Haese Michael Haese cyan magenta yellow 95 100 50 75 25 0 5 95 100 50 75 25 0 5 95 100 50 75 25 0 5 95 100 50 75 25 0 5 for use with IB Diploma Programme black Y:\HAESE\IB_HL_OPT-DM\IB_HL_OPT-DM_00\001IB_HL_OPT-DM_00.cdr Friday, 21 February 2014 11:33:09 AM BRIAN IB_HL-3ed MATHEMATICS FOR THE INTERNATIONAL STUDENT Mathematics HL (Option): Discrete Mathematics Catherine Quinn Peter Blythe Chris Sangwin Robert Haese Michael Haese B.Sc.(Hons), Grad.Dip.Ed., Ph.D. B.Sc. M.A., M.Sc., Ph.D. B.Sc. B.Sc.(Hons.), Ph.D. Haese Mathematics 152 Richmond Road, Marleston, SA 5033, AUSTRALIA Telephone: +61 8 8210 4666, Fax: +61 8 8354 1238 Email:
[email protected] www.haesemathematics.com.au Web: National Library of Australia Card Number & ISBN 978-1-921972-34-8 © Haese & Harris Publications 2014 Published by Haese Mathematics. 152 Richmond Road, Marleston, SA 5033, AUSTRALIA First Edition 2014 Artwork by Brian Houston. Cover design by Piotr Poturaj. Typeset in Australia by Deanne Gallasch. Typeset in Times Roman 10. Computer software by Tim Lee. Production work by Anna Rijken and Mark Humphries. Printed in China by Prolong Press Limited. The textbook and its accompanying CD have been developed independently of the International Baccalaureate Organization (IBO). The textbook and CD are in no way connected with, or endorsed by, the IBO. This book is copyright. Except as permitted by the Copyright Act (any fair dealing for the purposes of private study, research, criticism or review), no part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher. Enquiries to be made to Haese Mathematics. Copying for educational purposes: Where copies of part or the whole of the book are made under Part VB of the Copyright Act, the law requires that the educational institution or the body that administers it has given a remuneration notice to Copyright Agency Limited (CAL). For information, contact the Copyright Agency Limited. Acknowledgements: While every attempt has been made to trace and acknowledge copyright, the authors and publishers apologise for any accidental infringement where copyright has proved untraceable. They would be pleased to come to a suitable agreement with the rightful owner. cyan magenta yellow 95 100 50 75 25 0 5 95 100 50 75 25 0 5 95 100 50 75 25 0 5 95 100 50 75 25 0 5 Disclaimer: All the internet addresses (URLs) given in this book were valid at the time of printing. While the authors and publisher regret any inconvenience that changes of address may cause readers, no responsibility for any such changes can be accepted by either the authors or the publisher. black Y:\HAESE\IB_HL_OPT-DM\IB_HL_OPT-DM_00\002IB_HL_OPT-DM_00.cdr Thursday, 27 February 2014 3:46:23 PM BRI