Boolean Algebra and Its Applications

by J. Eldon Whitesitt

Overview

This introduction to Boolean algebra explores the subject on a level accessible even to those with a modest background in mathematics. The first chapter presents the algebra of sets from an intuitive point of view, followed by a formal presentation in chapter two of Boolean algebra as an abstract algebraic system, with no reference to applications.
Succeeding chapters offer concise accounts of applications to symbolic logic, focusing on topics of logic common to elementary mathematics and discussing concepts of valid argument and indirect proofs. Additional topics include the algebra of circuits — switching, relay, and computer — as well as the application of the algebra of sets to probability theory. Problems appear throughout the text, with answers to selected problems at the end of the book. Geared toward students of mathematics, computer science, and electrical engineering, this text can be appreciated by anyone who understands college-level mathematics. It will prove particularly valuable to philosophy students and others wishing to study symbolic logic and its applications to computer science.

Product Details

ISBN-13:	9780486477671
Publisher:	Dover Publications
Publication date:	03/18/2010
Series:	Dover Books on Computer Science
Pages:	182
Product dimensions:	5.40(w) x 8.50(h) x 0.50(d)

About the Author

A mathematics professor at Montana State University, J. Eldon Whitesitt received his doctorate from the University of Illinois, Urbana-Champaign. He is the author of several algebra texts published by Addison-Wesley.

Table of Contents

Chapter 1 The Algebra of Sets 1

1-1 Introduction 1

1-2 Element and set 1

1-3 The combination of sets 3

1-4 Venn diagrams 5

1-5 Fundamental laws 7

1-6 Expanding, factoring, and simplifying 9

1-7 Properties of set inclusion 12

1-8 Conditional equations 15

1-9 Solution of equations 19

1-10 The number of elements in a set 20

Chapter 2 Boolean Algebra 25

2-1 Introduction 25

2-2 Preliminary definitions 25

2-3 Definition and properties of a Boolean algebra 27

2-4 Disjunctive normal form 33

2-5 Conjunctive normal form 38

2-6 Representation of a Boolean algebra 41

Chapter 3 Symbolic Logic and the Algebra of Propositions 43

3-1 Introduction 43

3-2 Propositions and definitions of symbols 43

3-3 Truth tables 47

3-4 Object logic and syntax logic 52

3-5 Material implication 52

3-6 Truth sets for propositions 56

3-7 Quantifiers 59

3-8 Valid arguments 61

3-9 Indirect proofs 66

3-10 Functionally complete sets of operations 68

3-11 Special problems 70

Chapter 4 Switching Algebra 75

4-1 Introduction 75

4-2 Definition of the algebraic symbols 75

4-3 Simplification of circuits 79

4-4 Non-series-parallel circuits 83

4-5 Design of circuits from given properties 90

4-6 Design of n-terminal circuits 94

4-7 Symmetric functions and their circuits 99

Chapter 5 Relay Circuits and Control Problems 104

5-1 Introduction 104

5-2 Basic relay control paths 106

5-3 n-terminal circuits and the uses of transfer contacts 110

5-4 Operate and hold paths 116

5-5 Sequential circuits and sequence diagrams 119

5-6 Design of sequential relay circuits from given conditions 124

5-7 Special problems involving the design of relay circuits 132

Chapter 6 Circuits for Arithmetic Computation 135

6-1 Introduction 135

6-2 The binary number system 135

6-3 Logical circuit elements 138

6-4 Addition of binary numbers 142

6-5 Subtraction of binary numbers 145

6-6 Accumulation 147

6-7 Binary multiplication 150

Chapter 7 Introduction to Probability in Finite Sample Spaces 153

7-1 Introduction 153

7-2 Event, sample space, probability 153

7-3 Conditional probability 157

7-4 Some aids to counting 160

7-5 Bernoulli trials, binomial distribution 163

Answers to Selected Problems 168

Index 179