Precize Discrete Mathematical Structure

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The present book is the culmination of honest and sincere efforts on the part of the author to meet the requirements of students who study Discrete Mathematics in BCA. The entire subject matter has been arranged in a systematic, graded, simple, lucid and exhaustive manner to meet the various needs of all types of learners. Each chapter begins with some definitions followed by theorems with complete proofs and solved problems so that the study leads to perfect clarity and understanding. A large number of notes and remarks have been added for a better understanding of the subject. Well-planned and exhaustive exercises have been given in each chapter to provide the students with an opportunity of exhaustive practice.

A serious effort has been made to keep the book free from errors, but even then some errors might have crept in. Suggestions for the improvement of the book will be gratefully acknowledged.

The authors are indebted to a number of colleagues and students for their valuable critical comments and for the help rendered by them in the preparation of the manuscript.


Set Theory : Relations and Functions : Set Notation and Description, subset, basic set operations, Venn Diagrams, laws of set theory, partitions of sets, minsets, duality principle, basic definitions of relations and functions, graphics of relations, properties of relations : injective, surjective and bijective functions, compositions.

Recurrence : Recurrence Relations and Recursive Algorithms – Linear-RecurrenceRelations with Constant Coefficients; Homogeneous Solutions : Particular Solution, Total Solution, Solution by the Method of Generating functions.

Graph Theory : Graph and planar graphs – Basic Terminology, Multi-raphs,

Weighted Graphs, Paths and Circuits, Shortest Paths, Eulerian Paths and Circuits. Travelling Salesman Problem, Planar Graphs.

Automata Theory : Finite State Machines–Equivalent Machines, Finite State Machines as language Recognizers; Analysis of Algorithms – Time Complexity, Complexity of Problems.


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