Cover -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- List of Symbols -- Chapter 1. Mathematical Logic -- 1.0 Introduction -- 1.1 Statement (Proposition) -- 1.2 Logical Connectives -- 1.3 Conditional -- 1.4 Bi-Conditional -- 1.5 Converse -- 1.6 Inverse -- 1.7 Contra Positive -- 1.8 Exclusive OR -- 1.9 NAND -- 1.10 NOR -- 1.11 Tautology -- 1.12 Contradiction -- 1.13 Satisfiable -- 1.14 Duality Law -- 1.15 Algebra of Propositions -- 1.16 Mathematical Induction -- Solved Examples -- Exercises -- Chapter 2. Set Theory -- 2.0 Introduction -- 2.1 Sets -- 2.2 Types of Sets -- 2.3 Cardinality of a Set -- 2.4 Subset and Superset -- 2.5 Comparability of Sets -- 2.6 Power Set -- 2.7 Operations on Sets -- 2.8 Disjoint Sets -- 2.9 Application of Set Theory -- 2.10 Product of Sets -- 2.11 Fundamental Products -- Solved Examples -- Exercises -- Chapter 3. Binary Relation -- 3.0 Introduction -- 3.1 Binary Relation -- 3.2 Inverse Relation -- 3.3 Graph of Relation -- 3.4 Kinds of Relation -- 3.5 Arrow Diagram -- 3.6 Void Relation -- 3.7 Identity Relation -- 3.8 Universal Relation -- 3.9 Relation Matrix (Matrix of the Relation) -- 3.10 Composition of Relations -- 3.11 Types of Relations -- 3.12 Types of Relations and Relation Matrix -- 3.13 Equivalence Relation -- 3.14 Partial Order Relation -- 3.15 Total Order Relation -- 3.16 Closures of Relations -- 3.17 Equivalence Classes -- 3.18 Partitions -- Solved Examples -- Exercises -- Chapter 4. Function -- 4.0 Introduction -- 4.1 Function -- 4.2 Equality of Functions -- 4.3 Types of Function -- 4.4 Graph of Function -- 4.5 Composition of Functions -- 4.6 Inverse Function -- 4.7 Some Important Functions -- 4.8 Hash Function -- Solved Examples -- Exercises -- Chapter 5. Generating Function and Recurrence Relation -- 5.0 Introduction -- 5.1 Generating Functions -- 5.2 Partitions of Integers.

5.3 Recurrence Relations -- 5.4 Models of Recurrence Relation -- 5.5 Linear Recurrence Relation With Constant Coefficients -- 5.6 Different Methods of Solution -- 5.7 Homogeneous Solutions -- 5.8 Particular Solution -- 5.9 Total Solution -- 5.10 Solution by Generating Function -- 5.11 Analysis of the Algorithms -- Solved Examples -- Exercises -- Chapter 6. Combinatorics -- 6.0 Introduction -- 6.1 Fundamental Principle of Counting -- 6.2 Factorial Notation -- 6.3 Permutation -- 6.4 Combination -- 6.5 The Binomial Theorem -- 6.6 Binomial Theorem for Rational Index -- 6.7 The Catalan Numbers -- 6.8 Ramsey Number -- Chapter 7. Group Theory -- 7.0 Introduction -- 7.1 Binary Operation On a Set -- 7.2 Algebraic Structure -- 7.3 Group -- 7.4 Subgroup -- 7.5 Cyclic Group -- 7.6 Cosets -- 7.7 Homomorphism -- Solved Examples -- Exercises -- Chapter 8. Codes and Group Codes -- 8.0 Introduction -- 8.1 Terminologies -- 8.2 Error Correction -- 8.3 Group Codes -- 8.4 Weight of Code Word -- 8.5 Distance Between the Code Words -- 8.6 Error Correction for Block Code -- 8.7 Cosets -- Solved Examples -- Exercises -- Chapter 9. Ring Theory -- 9.0 Introduction -- 9.1 Ring -- 9.2 Special Types of Ring -- 9.3 Ring Without Zero Divisor -- 9.4 Integral Domain -- 9.5 Division Ring -- 9.6 Field -- 9.7 The Pigeonhole Principle -- 9.8 Characteristics of a Ring -- 9.9 Sub Ring -- 9.10 Homomorphism -- 9.11 Kernal of Homomorphism of Ring -- 9.12 Isomorphism -- Solved Examples -- Exercises -- Chapter 10 Boolean Algebra -- 10.1 Introduction -- 10.1 Gates -- 10.2 More Logic Gates -- 10.3 Combinatorial Circuit -- 10.4 Boolean Expression -- 10.5 Equivalent Combinatorial Cricuits -- 10.6 Boolean Algebra -- 10.7 Dual of a Statement -- 10.8 Boolean Function -- 10.9 Various Normal Forms -- Solved Examples -- Exercises -- Chapter 11. Introduction of Lattices -- 11.0 Introduction.

11.1 Lattices -- 11.2 Hasse Diagram -- 11.3 Principle of Duality -- 11.4 Distributive Lattice -- 11.5 Bounded Lattice -- 11.6 Complemented Lattice -- 11.7 Some Special Lattices -- Solved Examples -- Exercises -- Chapter 12. Graph Theory -- 21.0 Introduction -- 12.1 Graph -- 12.2 Kinds of Graph -- 12.3 Digraph -- 12.4 Weighted Graph -- 12.5 Degree of a Vertex -- 12.6 Path -- 12.7 Complete Graph -- 12.8 Regular Graph -- 12.9 Cycle -- 12.10 Pendant Vertex -- 12.11 Acyclic Graph -- 12.12 Matrix Representation of Graphs -- 12.13 Connected Graph -- 12.14 Graph Isomorphism -- 12.15 Bipartite Graph -- 12.16 Subgraph -- 12.17 Walks -- 12.18 Operations on Graphs -- 12.19 Fusion of Graphs -- Solved Examples -- Exercises -- Chapter 13. Tree -- 13.0 Introduction -- 13.1 Tree -- 13.2 Fundamental Terminologies -- 13.3 Binary Tree -- 13.4 Bridge -- 13.5 Distance and Eccentricity -- 13.6 Central Point and Centre -- 13.7 Spanning Tree -- 13.8 Searching Algorithms -- 13.9 Shortest Path Algorithms -- 13.10 Cut Vertices -- 13.11 Euler Graph -- 13.12 Hamiltoniah Path -- 13.13 Closure of a Graph -- 13.14 Travelling Salesman Problem -- Solved Examples -- Exercises -- Chapter 14 Fuzzy Set Theory -- 14.0 Introduction -- 14.1 Fuzzy Versus Crisp -- 14.2 Fuzzy Sets -- 14.3 Basic Definitions -- 14.4 Basic Operations on Fuzzy Sets -- 14.5 Properties of Fuzzy Sets -- 14.6 Interval Valued Fuzzy Set -- 14.7 Operations on l-v Fuzzy Sets -- 14.8 Fuzzy Relations -- 14.9 Operations on Fuzzy Relations -- 14.10 Fuzzy Logic -- Solved Examples -- Exercises -- References -- Index.