Mathematical Foundations of Computer Science
eBook - ePub

Mathematical Foundations of Computer Science

  1. 440 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

Mathematical Foundations of Computer Science

About this book

This book presents topics from mathematics which are relevant and useful to computer science. This book treats basic topics such as number theory, set theory, functions etc. in a simple way. Each chapter has been planned as independent unit so that various interrelated topics can also be read independently. Ample amount of examples and problems are given at the end of each chapter to help both the students and researchers. Hints and answers are also given for the problems in the exercise to help the students for self-learning.

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Yes, you can access Mathematical Foundations of Computer Science by Bhavanari Satyanarayana,T.V. Pradeep Kumar,Shaik Mohiddin Shaw in PDF and/or ePUB format, as well as other popular books in Computer Science & Computer Science General. We have over one million books available in our catalogue for you to explore.

Information

Publisher
CRC Press
Year
2019
Print ISBN
9780367366810
eBook ISBN
9781000702712
Edition
1
Topic
Computer Science
Subtopic
Computer Science General
Index
Computer Science

CHAPTER - 1

Propositional Calculus

LEARNING OBJECTIVES
♦ to Construct compound statements by using the connectives
♦ to identify the Tautologies and Contradictions
♦ to Construct the Truth Tables for the given expressions
♦ to find the Equivalent statements for a given expression
♦ to formulate DNF and CNF for the given expressions

Introduction

Logic means reasoning. One of the important aims of logic is to provide rules through which one can determine the validity of any particular argument. Logic concern with all types of reasonings such as legal arguments, mathematical proofs, conclusions in a scientific theory based upon a set of given hypothesis. The rules are called as rules of inference. The rules should be independent of any particular argument or discipline or language used in the argument.
We shall mean, by formal logic, a system of rules and procedures used to decide whether or not a statement follows from some given set of statements.
In order to avoid ambiguity, we use symbols. The symbols are easy to write and easy to manipulate. Hence, the logic that we study is named as “Symbolic logic”. For example, observe the following statements.
(i) All men are mortal
(ii) Socrates is a man
Therefore (iii) Socrates is mortal
According to the logic, if any three statements have the following form...

Table of contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright Page
  5. Preface
  6. Acknowledgement
  7. Table of Contents
  8. Chapter 1: Propositional Calculus
  9. Chapter 2: Predicate Calculus
  10. Chapter 3: Number Theory
  11. Chapter 4: Mathematical Induction
  12. Chapter 5: Set Theory
  13. Chapter 6: Functions
  14. Chapter 7: Graph Theory - I
  15. Chapter 8: Graph Theory - II
  16. Chapter 9: Graph Theory - III
  17. Chapter 10: Graph Theory - IV
  18. Chapter 11: Algebraic Structures
  19. Chapter 12: Algebraic Structures (Groups and Rings)
  20. Chapter 13: Permutations and Combinations
  21. Chapter 14: Binomial Theorem
  22. Chapter 15: Recurrence Relations
  23. Chapter 16: Some Methods of Solving Recurrence Relations
  24. Bibliography