Logic and Boolean Algebra

By: BRADFORD H ARNOLD

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Paperback | 20 October 2011

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160 Pages

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22.9 x 15.2 x 1.27

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This volume concentrates on the structure of Boolean algebras and rings as developed through simpler algebraic systems. The algebra of logic and set theory appears as applications or illustrations throughout, and numerous problems form an integral part of the text. No prior knowledge of Boolean algebra is necessary.
The text begins with a consideration of some concepts of intuitive logic. Subsequent chapters introduce Boolean functions, basic ordered sets, and a succession of algebraic systems. An examination of the principle of duality leads to a final chapter on applications, including electrical networks and computer design. Suitable for courses in computer design, circuit analysis, and switching circuits, this volume can also serve as a reference for professionals.

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Non-Fiction Mathematics Algebra Mathematical Foundation Mathematical Logic

Some Concepts of Intuitive Logic	p. 1
Introduction	p. 1
Sentences and Connectives	p. 2
Variables and Functions	p. 9
Related Sentential Functions; Truth Value Functions	p. 16
Some Methods of Proof	p. 20
Boolean Functions	p. 27
Introduction	p. 27
Basic Definitions; Use of Tables	p. 28
Equivalence Relations	p. 32
Correspondence between Truth Value Functions and Boolean Functions	p. 37
Ordered Sets	p. 41
Introduction	p. 41
Basic Definition; Graphical Representation	p. 41
Isomorphism	p. 47
The Ordering in B_n	p. 50
Connection with Logic	p. 51
Lattices	p. 55
Introduction	p. 55
Basic Definitions	p. 56
Further Properties of Lattices	p. 60
The Lattice B_n and Applications to Logic	p. 65
Boolean Algebras	p. 71
Introduction	p. 71
Basic Definition and Properties	p. 71
Representation in Terms of Subsets of a Set	p. 76
B_n as a Boolean Algebra; Applications to Logic	p. 81
Boolean Rings	p. 83
Introduction	p. 83
Definitions and Basic Properties	p. 84
Boolean Rings with a Unit Element are Equivalent to Boolean Algebras	p. 89
Representation of a Finite Boolean Ring in Terms of n-tuples of Boolean Constants	p. 95
Normal Forms, Duality	p. 101
Introduction	p. 101
Disjunctive and Conjunctive Normal Forms	p. 102
The Ring Normal Form	p. 109
Normal Forms in B_n	p. 114
Duality	p. 117
Some Applications of Boolean Algebra	p. 121
Introduction	p. 121
Applications to Electrical Networks	p. 122
Applications to Computer Design	p. 128
Applications to Logic	p. 133
References	p. 139
Index	p. 143
Table of Contents provided by Ingram. All Rights Reserved.

Logic and Boolean Algebra

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