Table Of ContentLogic
DeMYSTiFieD®
DeMYSTiFieD® Series
Accounting Demystified Logic Demystified
Advanced Calculus Demystified Macroeconomics Demystified
Advanced Physics Demystified Management Accounting Demystified
Advanced Statistics Demystified Math Proofs Demystified
Algebra Demystified Math Word Problems Demystified
Alternative Energy Demystified MATLAB® Demystified
Anatomy Demystified Medical Billing and Coding Demystified
asp.net 2.0 Demystified Medical Terminology Demystified
Astronomy Demystified Meteorology Demystified
Audio Demystified Microbiology Demystified
Biology Demystified Microeconomics Demystified
Biotechnology Demystified Nanotechnology Demystified
Business Calculus Demystified Nurse Management Demystified
Business Math Demystified OOP Demystified
Business Statistics Demystified Options Demystified
C++ Demystified Organic Chemistry Demystified
Calculus Demystified Personal Computing Demystified
Chemistry Demystified Pharmacology Demystified
Circuit Analysis Demystified Physics Demystified
College Algebra Demystified Physiology Demystified
Corporate Finance Demystified Pre-Algebra Demystified
Databases Demystified Precalculus Demystified
Data Structures Demystified Probability Demystified
Differential Equations Demystified Project Management Demystified
Digital Electronics Demystified Psychology Demystified
Earth Science Demystified Quality Management Demystified
Electricity Demystified Quantum Mechanics Demystified
Electronics Demystified Real Estate Math Demystified
Engineering Statistics Demystified Relativity Demystified
Environmental Science Demystified Robotics Demystified
Everyday Math Demystified Sales Management Demystified
Fertility Demystified Signals and Systems Demystified
Financial Planning Demystified Six Sigma Demystified
Forensics Demystified Spanish Demystified
French Demystified sql Demystified
Genetics Demystified Statics and Dynamics Demystified
Geometry Demystified Statistics Demystified
German Demystified Technical Analysis Demystified
Home Networking Demystified Technical Math Demystified
Investing Demystified Trigonometry Demystified
Italian Demystified uml Demystified
Java Demystified Visual Basic 2005 Demystified
JavaScript Demystified Visual C# 2005 Demystified
Lean Six Sigma Demystified XML Demystified
Linear Algebra Demystified
Logic
DeMYSTiFieD®
anthony Boutelle
Stan Gibilisco
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About the Authors
Anthony Boutelle is a graduate of Macalester College in St. Paul, Minnesota,
with a major in philosophy and a minor in physics. He currently works as a
technical reviewer and editor for a computer firm in Minneapolis.
Stan Gibilisco is an electronics engineer, researcher, and mathematician who
has authored several titles for the McGraw-Hill Demystified and Know-It-All
series, along with dozens of other books on diverse technical topics.
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Contents
PPrreeffaaccee xxvviiii
chapter 1 Arguments, Validity, and Truth Tables 1
What’s Logic About? 2
Terminology 2
Logical Arguments 2
What’s Logic Good For? 3
Logical Form 3
An Example 4
When Truth Doesn’t Matter 4
When Meaning Doesn’t Matter 4
Rules for Reasoning 5
Identity 5
Contradiction 6
True or False 6
Sentence Forms 6
Subject/Verb (SV) Statements 6
Subject/Verb/Object (SVO) Statements 7
Subject/Linking Verb/Complement (SLVC) Statements 7
Symbols and Operations 8
Logical Negation (NOT) 8
Logical Conjunction (AND) 9
Inclusive Logical Disjunction (OR) 9
Exclusive Logical Disjunction (XOR) 10
Logical Implication (IF/THEN) 11
Logical Equivalence (IFF) 12
vii
viii LOGIC DeMYSTiFieD
Tables for Basic Operations 14
Table for Logical Negation 14
Table for Conjunction 14
Tables for Logical Disjunction 15
Table for Logical Implication 15
Table for Logical Equivalence 16
A Quick Proof 17
Precedence 18
Examples of Precedence 19
Proofs Using Truth Tables 20
Reversing the Order of a Conjunction 21
Grouping of Conjunctions 21
Reversing the Order of an Inclusive Disjunction 23
Grouping of Inclusive Disjunctions 23
Reversing the Order of an Implication 25
Ungrouping the Negation of a Conjunction 25
Ungrouping the Negation of an Inclusive
Disjunction 26
Regrouping with Mixed Operations 27
Truth Tables Have Power! 27
Quiz 31
chapter 2 Propositional Logic 33
A Formal System 34
Propositional Formulas (PFs) 34
Is This Mathematics? 35
Contradiction 35
Sequents 36
Backing Up the Argument 37
Assumption (A) 37
Double Negation (DN) 38
Conjunction Introduction (ŸI) 39
Conjunction Elimination (ŸE) 39
Disjunction Introduction (⁄I) 40
Disjunction Elimination (⁄E) 40
Conditional Proof (CP) and Theorems 42
Biconditional Introduction (´I) 44
Biconditional Elimination (´E) 45
Substitution 45
Laws 48
Law of Contradiction 48
Law of Excluded Middle 48
Contents ix
Law of Double Negation 49
Commutative Laws 49
Associative Laws 50
Law of Implication Reversal 51
DeMorgan’s Laws 53
Distributive Laws 54
Interderivability ( ), Deriving Laws, and
Theorem Introduction (TI) 54
Quiz 57
chapter 3 Predicate Logic 61
Symbolizing Sentence Structure 62
Formal Predicates 62
Formal Subjects: Names 62
Formal Subjects: Variables 62
Predicate Sentence Formulas 63
More Predicate Sentences 64
Identity (=) 65
Building More Complex Formulas 65
Quantified Statements 66
Some versus All 66
The Existential Quantifier ($) 67
The Universal Quantifier (") 68
The Universe 68
Multiple Quantifiers 70
Translating the Quantifiers 72
Laws of Quantifier Transformation 72
Logical Relationships: The Square
of Opposition 73
Well-Formed Formulas 74
Properties of Two-Part Relations 75
Symmetry 75
Asymmetry 76
Antisymmetry 76
Nonsymmetry 76
Reflexivity 77
Irreflexivity 77
Nonreflexivity 77
Transitivity 77
Intratransitivity 78
Nontransitivity 78
Equivalence Relations 78
