Mathematics for Computer Science I (Descrete Mathematics).

MATHEMATICS FOR
COMPUTER
SCIENCE I
(DISCRETE MATHEMATICS)
Zuraida Abal Abas
Burhanuddin Mohd Aboobaider
Abdul Samad Hasan Basari
Editor
Ahmad Fadzli Nizam Abdul Rahman
Faculty of Information and Communication Technology,
Kolej Universiti Teknikal Kebangsaan Malaysia,
Karung Berkunci 1200,
75450 Melaka,
Malaysia.
© FTMK, KUTKM 2006
All rights reserved. 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 either the prior written permission
of the publisher.
The programs in this book have been included for their

instructional value. They have been tested with care but are not
guaranteed for any particular purpose. The author or publisher
does not offer any warranties or representations nor does it
accept any liabilities with respect to the programs.

STUDENT NAME:
MATRIC NUMBER:
SEMESTER:
COURSE:
YEAR / SEMESTER SESSION:

i

TABLE OF CONTENTS
PAGE
PREFACE

1

TUTORIAL 1: LOGIC, SETS AND FUNCTIONS

1.1
Objectives
1.2
Theoretical background
1.3
Examples
1.4
Tutorial questions: Logic, sets and functions
1.5
Quiz: Logic, set and functions

2

TUTORIAL 2: ALGORITHM AND INTEGERS
2.1
Objectives
2.2
Theoretical background
2.3
Examples

2.4
Tutorial questions: Algorithm and Integers
2.5
Quiz: Algorithm and Integers

34

TUTORIAL 3: MATHEMATICAL REASONING, INDUCTION AND
RECURSION
53
3.1
Objectives
3.2
Theoretical background
3.3
Examples
3.4
Tutorial questions: Mathematical reasoning, induction and
recursion
3.5

Quiz: Mathematical reasoning, induction and recursion
TUTORIAL 4: COUNTING
4.1
Objectives
4.2
Theoretical background
4.3
Examples
4.4
Tutorial questions: Counting
4.5
Quiz: Counting

70

ii

TABLE OF CONTENTS
PAGE
TUTORIAL 5: RELATIONS

5.1
Objectives
5.2
Theoretical background
5.3
Examples
5.4
Tutorial questions: Relations
5.5
Quiz: Relations

87

TUTORIAL 6: GRAPHS
6.1
Objectives
6.2
Theoretical background
6.3
Examples

6.4
Tutorial questions: Graphs
6.5
Quiz: Graphs

105

TUTORIAL 7: TREES
7.1
Objectives
7.2
Theoretical background
7.3
Examples
7.4
Quiz: Trees and Boolean Algebra

128

REFERENCES

150

iii

PREFACE

Overview
This module is intended for half of the course in Mathematics for Computer Science 1.
The module includes theoretical background, examples, exercises/tutorials, figures and
tables to help the first year student in Faculty of Information and Communication
Technology, Kolej Universiti Teknikal Kebangsaan Malaysia, master introductory
discrete mathematics.
Approach
This module has been guided by the following principles.
 To develop ideas step by step, leading from one idea to the next where possible, and
present material in a manner that will be easy to follow for all students.
 To use plenty of examples and exercises to reinforce students in understanding
discrete mathematics.
Chapter Layout

Each chapter begins with a list of objectives. These include the important concepts to be
mastered within the chapter. Extensive self-review questions are included at the end of
each chapter for self-study. They provide the student with a chance to build confidence
to answer quizes. This module contains 7 chapters i.e. chapter 1: Logic, sets and
functions, chapter 2: Algorithm and integers, chapter 3: Mathematical reasoning,
induction and recursion, chapter 4: Counting, chapter 5: Relations, Chapter 6: Graphs
and Chapter 7: Trees.

1