Author:
Dr.K.KUPPUSAMY
Professor and Head (i/c),
Dept. of Computational Logistics,
Science Campus,
Alagappa University,
Karaikudi– 630 003.
“The Copyright shall be vested with Alagappa University”
All rights reserved. No part of this publication which is material protected by this copy right notice may
be reproduced or transmitted or utilized or stored in any form or by any means now known or
hereinafter invented, electronic, digital or mechanical, including photocopying, scanning, recording or
by any information storage or retrieval system, without prior written permission from the Alagappa
University, Karaikudi, Tamil Nadu.
, SYLLABUS - BOOK MAPPING TABLE
DISCRETE MATHEMATICS
UNIT SYLLABUS MAPPING IN
BOOK
BLOCK 1 : MATHEMATICAL LOGIC
1 Mathematical Logic: Statements And Notation - Pages1-48
Connectives -Normal Forms –The Theory Of Inference
for the Statement Calculus.
2 Predicate Calculus: The Predicate Calculus - Pages 49-65
Inference Theory and Predicate Calculus.
3 Set Theory: Sets – Basic Concepts – Notation - Pages 66-83
Inclusion And Equality of Sets – The Power Set. power se
BLOCK 2 : RELATIONS
4 Relations and Ordering Properties –Relation Matrix Pages 84-97
And Graph of a Relation.
5 Relations Partition –Equivalence and Compatibility Pages 98-111
Relations.
6 Composition and Partial Ordering: Composition – Pages 112-127
Partial Ordering –Partially Ordered Set. Ordered
BLOCK 3 : FUNCTIONS
7 Functions –Definition –Composition –Inverse –Binary Pages 128-146
And N-Ary Operations
8 Other Functions : Characteristic Function –Hashing Pages 147-156
Function.
BLOCK 4 : ALGEBRAIC STRUCTURES
9 Algebraic Structures: Algebraic Systems: Examples Pages157-166
And General Properties.
10 Semigroups and Monoids: Definitions and Pages167-178
Examples-Homomorphism of Semigroups and
Monoids - Subsemigroups and Submonoids.
11 Groups: Definitions And Examples - Cosets and Pages 179-194
theorem lagrange’s.
12 Normal Subgroups –Algebraic Systems with Two Pages 195-206
Binary Operations.
i
, BLOCK 5 : GRAPH AND FINITE PROBABILITY
13 Graphtheory: Basic Concepts –Definition –Paths Pages 207–246
Reach -Ability and Connectedness –Matrix
Representation of Graphs - Trees.
14 Finite Probability– Probability Distributions Pages 247– 271
Conditional Probability Independence –Bayes’–
Theorem Mathematical Expectation.
ii
, CONTENTS
BLOCK 1 : MATHEMATICAL LOGIC
1 –48
UNIT : 1 MATHEMATICAL LOGIC
1.0 Introduction
1.1 Objectives
1.2 Statements and Notation
1.3 Connectives
1.4 Normal Forms
1.5 The Theory of Inference for the Statement Calculus.
1.6 Check Your Progress Questions
1.7 Answers to Check Your Progress Questions
1.8 Summary
1.9 Key Words
1.10 Self Assessment Questions and Exercises
1.11 Further Readings
UNIT : 2 PREDICATE CALCULUS 49-65
2.0 Introduction
2.1 Objectives
2.2 The Predicate Calculus
2.3 Inference Theory and Predicate Calculus.
2.4 Check Your Progress Questions
2.5 Answers to Check Your Progress Questions
2.6 Summary
2.7 Key Words
2.8 Self Assessment Questions and Exercises
2.9 Further Readings
UNIT : 3 SET THEORY 66-83
3.0 Introduction
3.1 Objectives
3.2 Sets
3.3 Notation
3.4 Inclusion and Equality of Sets
3.5 The Power Set
3.6 Venn Diagram
3.7 Check Your Progress Questions
3.9 Answers to Check Your Progress Questions
3.10 Summary
3.11 Key Words
3.12 Self Assessment Questions and Exercises
3.13 Further Readings
iii
Dr.K.KUPPUSAMY
Professor and Head (i/c),
Dept. of Computational Logistics,
Science Campus,
Alagappa University,
Karaikudi– 630 003.
“The Copyright shall be vested with Alagappa University”
All rights reserved. No part of this publication which is material protected by this copy right notice may
be reproduced or transmitted or utilized or stored in any form or by any means now known or
hereinafter invented, electronic, digital or mechanical, including photocopying, scanning, recording or
by any information storage or retrieval system, without prior written permission from the Alagappa
University, Karaikudi, Tamil Nadu.
, SYLLABUS - BOOK MAPPING TABLE
DISCRETE MATHEMATICS
UNIT SYLLABUS MAPPING IN
BOOK
BLOCK 1 : MATHEMATICAL LOGIC
1 Mathematical Logic: Statements And Notation - Pages1-48
Connectives -Normal Forms –The Theory Of Inference
for the Statement Calculus.
2 Predicate Calculus: The Predicate Calculus - Pages 49-65
Inference Theory and Predicate Calculus.
3 Set Theory: Sets – Basic Concepts – Notation - Pages 66-83
Inclusion And Equality of Sets – The Power Set. power se
BLOCK 2 : RELATIONS
4 Relations and Ordering Properties –Relation Matrix Pages 84-97
And Graph of a Relation.
5 Relations Partition –Equivalence and Compatibility Pages 98-111
Relations.
6 Composition and Partial Ordering: Composition – Pages 112-127
Partial Ordering –Partially Ordered Set. Ordered
BLOCK 3 : FUNCTIONS
7 Functions –Definition –Composition –Inverse –Binary Pages 128-146
And N-Ary Operations
8 Other Functions : Characteristic Function –Hashing Pages 147-156
Function.
BLOCK 4 : ALGEBRAIC STRUCTURES
9 Algebraic Structures: Algebraic Systems: Examples Pages157-166
And General Properties.
10 Semigroups and Monoids: Definitions and Pages167-178
Examples-Homomorphism of Semigroups and
Monoids - Subsemigroups and Submonoids.
11 Groups: Definitions And Examples - Cosets and Pages 179-194
theorem lagrange’s.
12 Normal Subgroups –Algebraic Systems with Two Pages 195-206
Binary Operations.
i
, BLOCK 5 : GRAPH AND FINITE PROBABILITY
13 Graphtheory: Basic Concepts –Definition –Paths Pages 207–246
Reach -Ability and Connectedness –Matrix
Representation of Graphs - Trees.
14 Finite Probability– Probability Distributions Pages 247– 271
Conditional Probability Independence –Bayes’–
Theorem Mathematical Expectation.
ii
, CONTENTS
BLOCK 1 : MATHEMATICAL LOGIC
1 –48
UNIT : 1 MATHEMATICAL LOGIC
1.0 Introduction
1.1 Objectives
1.2 Statements and Notation
1.3 Connectives
1.4 Normal Forms
1.5 The Theory of Inference for the Statement Calculus.
1.6 Check Your Progress Questions
1.7 Answers to Check Your Progress Questions
1.8 Summary
1.9 Key Words
1.10 Self Assessment Questions and Exercises
1.11 Further Readings
UNIT : 2 PREDICATE CALCULUS 49-65
2.0 Introduction
2.1 Objectives
2.2 The Predicate Calculus
2.3 Inference Theory and Predicate Calculus.
2.4 Check Your Progress Questions
2.5 Answers to Check Your Progress Questions
2.6 Summary
2.7 Key Words
2.8 Self Assessment Questions and Exercises
2.9 Further Readings
UNIT : 3 SET THEORY 66-83
3.0 Introduction
3.1 Objectives
3.2 Sets
3.3 Notation
3.4 Inclusion and Equality of Sets
3.5 The Power Set
3.6 Venn Diagram
3.7 Check Your Progress Questions
3.9 Answers to Check Your Progress Questions
3.10 Summary
3.11 Key Words
3.12 Self Assessment Questions and Exercises
3.13 Further Readings
iii
