Discrete Mathematical Structure For BCA Course  (Paperback, Amrut Habib)

• This book is designed to meet the requirements of the students for Third semester B.C.A of Karnataka University.
• The topics include : Fundamental Principles of Countings. Fundamentals of Logic, Set Theory, Properties of Integers and Mathematical Induction and Relations and Functions.
• The subject has been presented in a simple, systematic, logical and lucid manner. Typical, standard and uniformly graded problems are solved at a level that an average student can grasp the knowledge.
• Large number of problems and examination questions based on past examination papers are included in the relevant chapters. Number of questions in exercises with answers are provided at the end of each chapter.
• Suggestions and corrections if any, are welcome.

Table of Contents
1. Fundamental Principles of Counting
1.1 Introduction
1.2 The Rule of Sum
1.3 The Rule of Product
1.4 Permutations
1.5 Permutations with Repetations
1.6 Combinations
1.7 Combinations with Repetation
1.8 The Binomial Theorem
Exercise
Answers
2. Fundamentals of Logic
2.1 Introduction
2.2 Propositions
2.3 Logical Connectives
2.4 Compound Propositions and Truth Tables
2.5 Tautology, Contradiction and Contingency
2.6 Logical Equivalence
2.7 Laws of Logic
2.8 Converse, Inverse and Contrapositive
2.9 Logical Implication
2.10 Rules of Inference
2.11 Quantifiers
2.12 Logical Implication involving Quantifiers
2.13 Proofs of Theorems
Exercise
Answers
3. Set Theory
3.1 Introduction
3.2 Operation on Sets
3.3 Laws of Sets
3.4 Countable and Uncountable Sets
3.5 Addition Principle
3.6 Probability
Exercise
Answers
4. Properties of Integers and Mathematical Induction
4.1 Introduction
4.2 The Well-Ordering Principle
4.3 Mathematical Induction
4.4 Recursive Definitions
4.5 Divisibility
4.6 Properties of Divisibility.
4.7 The Division Algorithm
4.8 Greatest Common Divisor (G.C.D)
4.9 Euclid's Algorithm for Finding Greatest Common Divisor
4.10 Prime Numbers, Composite Numbers and Relatively Prime Numbers
4.11 Fundamental Theorem of Arithmatic
4.12 The Number and the Sum of Positive Divisors of a given Number
Exercise
Answers
5. Relations and Functions
5.1 Cartesian Product of Sets
5.2 Relations
5.3 Functions
5.4 Types of Functions
5.5 Properties of Functions
5.6 Stirling Numbers of the Second Kind
5.7 Special Functions : Unary and Binary Operations
5.8 The Pigeonhole Principle
5.9 Composition of Functions
5.10 Theorems on Functions
5.11 Invertible Functions
5.12 Theorems on Invertible Functions
5.13 Operations on Relations
5.14 Compositions of Relations
5.15 Properties of Relations
Exercise