Boolean Algebra Essentials
Published on 1. January 2013
169 pages
978-0-7386-7167-3 (ISBN)
Description
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Boolean Algebra includes set theory, sentential calculus, fundamental ideas of Boolean algebras, lattices, rings and Boolean algebras, the structure of a Boolean algebra, and Boolean algebra in communication systems.
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Content
- Intro
- Title Page
- Copyright Page
- WHAT "THE ESSENTIALS" WILL DO FOR YOU
- Table of Contents
- CHAPTER 1 - SET THEORY
- 1.1 WHAT ARE SETS?
- 1.2 INCLUSION RELATIONS BETWEEN SETS
- 1.3 THE UNION AND INTERSECTION OF SETS
- 1.4 THE ALGEBRA OF SETS
- 1.5 MEASURING THE SIZE OF A SET
- 1.6 CARTESIAN PRODUCTS AND BINARY RELATIONS
- 1.7 ADDITIONAL SET THEORY CONCEPTS
- CHAPTER 2 - SENTENTIAL CALCULUS
- 2.1 FUNDAMENTAL CONCEPTS
- 2.2 TRUTH TABLES AND BASIC LOGICAL OPERATIONS
- 2.3 LOGICAL EQUIVALENCE
- 2.4 FUNDAMENTAL PROPERTIES OF OPERATIONS
- 2.5 SENTENCES, LITERALS AND FUNDAMENTAL CONJUNCTIONS
- 2.6 ADEQUATE SYSTEMS OF CONNNECTIVES AND DUALITY
- 2.7 LOGIC EQUIVALENCE CLASSES
- CHAPTER 3 - FUNDAMENTAL IDEAS OF BOOLEAN ALGEBRAS
- 3.1 PRELIMINARY REMARKS
- 3.2 DEFINITION OF A BOOLEAN ALGEBRA
- 3.3 BASIC PROPERTIES OF A BOOLEAN ALGEBRA
- 3.4 ORDER RELATIONS
- 3.5 REVERSE POLISH NOTATION
- 3.6 BOOLEAN FUNCTIONS
- CHAPTER 4 - LATTICES, RINGS AND BOOLEAN ALGEBRAS
- 4.1 BOOLEAN ALGEBRAS AND LATTICES
- 4.2 BOOLEAN ALGEBRAS AND RINGS
- CHAPTER 5 - THE STRUCTURE OF A BOOLEAN ALGEBRA
- 5.1 ISOMORPHISMS
- 5.2 COLLECTIONS OF SETS CLOSED UNDER UNION, INTERSECTION AND COMPLEMENT
- 5.3 ATOMS - BUILDING BLOCKS OF BOOLEAN ALGEBRAS
- 5.4 IDEALS - PARTITIONING A BOOLEAN ALGEBRA
- CHAPTER 6 - BOOLEAN ALGEBRA IN COMMUNICATIONS SYSTEMS
- 6.1 BACKGROUND REMARKS
- 6.2 SWITCHES AND CIRCUITS
