Discrete Mathematical Structures

A Succinct Foundation

B. V. Senthil Kumar, Hemen Dutta

• Publisher: CRC Press
• Year: 2019
• ISBN:
  9780429624308
• Edition: 1
• Topic: Computer Science
• Subtopic: Operating Systems
• Index: Computer Science

This book contains fundamental concepts on discrete mathematical structures in an easy to understand style so that the reader can grasp the contents and explanation easily. The concepts of discrete mathematical structures have application to computer science, engineering and information technology including in coding techniques, switching circuits, pointers and linked allocation, error corrections, as well as in data networking, Chemistry, Biology and many other scientific areas. The book is for undergraduate and graduate levels learners and educators associated with various courses and progammes in Mathematics, Computer Science, Engineering and Information Technology. The book should serve as a text and reference guide to many undergraduate and graduate programmes offered by many institutions including colleges and universities. Readers will find solved examples and end of chapter exercises to enhance reader comprehension.

Features

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• Offers comprehensive coverage of basic ideas of Logic, Mathematical Induction, Graph Theory, Algebraic Structures and Lattices and Boolean Algebra
• Provides end of chapter solved examples and practice problems
• Delivers materials on valid arguments and rules of inference with illustrations
• Focuses on algebraic structures to enable the reader to work with discrete structures

1

Logics and Proofs

1.1 Introduction

In this chapter, we discuss propositional logic and various methods of proving validity of propositions. The concept of logic has many applications in computer science to develop computer programs, to verify the logic of program and also in electronics to design circuits.

1.2 Proposition

A proposition (or statement) is a declarative sentence which is true or false, but not both. Consider, for example,

• (i) The year 2000 is a leap year.
• (ii) 5 + 3 = 7.
• (iii) x = 1 is a solution of x³ = 1.
• (iv) Close the door.

In the above, (i)–(iii) are propositions, whereas (iv) is not a proposition. Moreover, (i) and (iii) are true, while (ii) is false.

1.3 Compound Propositions

Many propositions are composite, that is, composed of subpropositions and various connectives discussed in the next section. Such composite propositions are called compound propositions. A...