Boolean Algebra and Its Applications PDF

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.

Chapter List (67 chapters):

• Chapter 1: Cover
• Chapter 2: Title Page
• Chapter 3: Copyright Page
• Chapter 4: Preface
• Chapter 5: Contents
• Chapter 6: Chapter 1. The Algebra of Sets
• Chapter 7: 1–1 Introduction
• Chapter 8: 1–2 Element and set
• Chapter 9: 1–3 The combination of sets
• Chapter 10: 1–4 Venn diagrams
• Chapter 11: 1–5 Fundamental laws
• Chapter 12: 1–6 Expanding, factoring, and simplifying
• Chapter 13: 1–7 Properties of set inclusion
• Chapter 14: 1–8 Conditional equations
• Chapter 15: 1–9 Solution of equations
• Chapter 16: 1–10 The number of elements in a set
• Chapter 17: Chapter 2. Boolean Algebra
• Chapter 18: 2–1 Introduction
• Chapter 19: 2–2 Preliminary definitions
• Chapter 20: 2–3 Definition and properties of a Boolean algebra
• Chapter 21: 2–4 Disjunctive normal form
• Chapter 22: 2–5 Conjunctive normal form
• Chapter 23: 2–6 Representation of a Boolean algebra
• Chapter 24: Chapter 3. Symbolic Logic and the Algebra of Propositions
• Chapter 25: 3–1 Introduction
• Chapter 26: 3–2 Propositions and definitions of symbols
• Chapter 27: 3–3 Truth tables
• Chapter 28: 3–4 Object logic and syntax logic
• Chapter 29: 3–5 Material implication
• Chapter 30: 3–6 Truth sets for propositions
• Chapter 31: 3–7 Quantifiers
• Chapter 32: 3–8 Valid arguments
• Chapter 33: 3–9 Indirect proofs
• Chapter 34: 3–10 Functionally complete sets of operations
• Chapter 35: 3–11 Special problems
• Chapter 36: Chapter 4. Switching Algebra
• Chapter 37: 4–1 Introduction
• Chapter 38: 4–2 Definition of the algebraic symbols
• Chapter 39: 4–3 Simplification of circuits
• Chapter 40: 4–4 Non-series-parallel circuits
• Chapter 41: 4–5 Design of circuits from given properties
• Chapter 42: 4–6 Design of n-terminal circuits
• Chapter 43: 4–7 Symmetric functions and their circuits
• Chapter 44: Chapter 5. Relay Circuits and Control Problems
• Chapter 45: 5–1 Introduction
• Chapter 46: 5–2 Basic relay control paths
• Chapter 47: 5–3 n-terminal circuits and the uses of transfer contacts
• Chapter 48: 5–4 Operate and hold paths
• Chapter 49: 5–5 Sequential circuits and sequence diagrams
• Chapter 50: 5–6 Design of sequential relay circuits from given conditions
• Chapter 51: 5–7 Special problems involving the design of relay circuits
• Chapter 52: Chapter 6. Circuits for Arithmetic Computation
• Chapter 53: 6–1 Introduction
• Chapter 54: 6–2 The binary number system
• Chapter 55: 6–3 Logical circuit elements
• Chapter 56: 6–4 Addition of binary numbers
• Chapter 57: 6–5 Subtraction of binary numbers
• Chapter 58: 6–6 Accumulation
• Chapter 59: 6–7 Binary multiplication
• Chapter 60: Chapter 7. Introduction to Probability in Finite Sample Spaces
• Chapter 61: 7–1 Introduction
• Chapter 62: 7–2 Event, sample space, probability
• Chapter 63: 7–3 Conditional probability
• Chapter 64: 7–4 Some aids to counting
• Chapter 65: 7–5 Bernoulli trials, binomial distribution
• Chapter 66: Answers to Selected Problems
• Chapter 67: Index

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