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CITATION

Boutelle, Tony and Gibilisco, Stan. Logic DeMYSTiFied. US: McGraw-Hill Professional, 2010.

Logic DeMYSTiFied

Authors: Tony Boutelle and Stan Gibilisco

Published:  October 2010

eISBN: 9780071701297 007170129X | ISBN: 9780071701280
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  • Contents
  • Preface
  • Chapter 1 Arguments, Validity, and Truth Tables
  • What's Logic About?
  • Terminology
  • Logical Arguments
  • What's Logic Good For?
  • Logical Form
  • An Example
  • When Truth Doesn't Matter
  • When Meaning Doesn't Matter
  • Rules for Reasoning
  • Identity
  • Contradiction
  • True or False
  • Sentence Forms
  • Subject/Verb (SV) Statements
  • Subject/Verb/Object (SVO) Statements
  • Subject/Linking Verb/Complement (SLVC) Statements
  • Symbols and Operations
  • Logical Negation (NOT)
  • Logical Conjunction (AND)
  • Inclusive Logical Disjunction (OR)
  • Exclusive Logical Disjunction (XOR)
  • Logical Implication (IF/THEN)
  • Logical Equivalence (IFF)
  • Tables for Basic Operations
  • Table for Logical Negation
  • Table for Conjunction
  • Tables for Logical Disjunction
  • Table for Logical Implication
  • Table for Logical Equivalence
  • A Quick Proof
  • Precedence
  • Examples of Precedence
  • Proofs Using Truth Tables
  • Reversing the Order of a Conjunction
  • Grouping of Conjunctions
  • Reversing the Order of an Inclusive Disjunction
  • Grouping of Inclusive Disjunctions
  • Reversing the Order of an Implication
  • Ungrouping the Negation of a Conjunction
  • Ungrouping the Negation of an Inclusive Disjunction
  • Regrouping with Mixed Operations
  • Truth Tables Have Power!
  • Quiz
  • Chapter 2 Propositional Logic
  • A Formal System
  • Propositional Formulas (PFs)
  • Is This Mathematics?
  • Contradiction
  • Sequents
  • Backing Up the Argument
  • Assumption (A)
  • Double Negation (DN)
  • Conjunction Introduction (ΛI)
  • Conjunction Elimination (ΛE)
  • Disjunction Introduction ((omitted)I)
  • Disjunction Elimination ((omitted)E)
  • Conditional Proof (CP) and Theorems
  • Biconditional Introduction ((omitted)I)
  • Biconditional Elimination ((omitted)E)
  • Substitution
  • Laws
  • Law of Contradiction
  • Law of Excluded Middle
  • Law of Double Negation
  • Commutative Laws
  • Associative Laws
  • Law of Implication Reversal
  • DeMorgan's Laws
  • Distributive Laws
  • Interderivability ((omitted)), Deriving Laws, and Theorem Introduction (TI)
  • Quiz
  • Chapter 3 Predicate Logic
  • Symbolizing Sentence Structure
  • Formal Predicates
  • Formal Subjects: Names
  • Formal Subjects: Variables
  • Predicate Sentence Formulas
  • More Predicate Sentences
  • Identity (=)
  • Building More Complex Formulas
  • Quantified Statements
  • Some versus All
  • The Existential Quantifier ((omitted))
  • The Universal Quantifier ((omitted))
  • The Universe
  • Multiple Quantifiers
  • Translating the Quantifiers
  • Laws of Quantifier Transformation
  • Logical Relationships: The Square of Opposition
  • Well-Formed Formulas
  • Properties of Two-Part Relations
  • Symmetry
  • Asymmetry
  • Antisymmetry
  • Nonsymmetry
  • Reflexivity
  • Irreflexivity
  • Nonreflexivity
  • Transitivity
  • Intratransitivity
  • Nontransitivity
  • Equivalence Relations
  • Predicate Proofs
  • Existential Introduction ((omitted)I)
  • Existential Elimination ((omitted)E)
  • Universal Introduction ((omitted)I)
  • Universal Elimination ((omitted)E)
  • Identity Introduction (=I)
  • Identity Elimination (=E)
  • Conventions for Predicate Proofs
  • Syllogisms
  • A Sample Syllogism
  • Allowed Propositions
  • Terms and Arguments
  • Conversion Laws
  • Classifying Syllogisms: Mood and Figure
  • Testing Syllogistic Arguments
  • Valid Syllogisms
  • Other Kinds of Syllogism
  • Quiz
  • Chapter 4 A Boot Camp for Rigor
  • Definitions
  • Elementary Terms
  • Line Segment
  • Half-Open Line Segment
  • Open Line Segment
  • Length of Line Segment
  • Closed-Ended Ray
  • Open-Ended Ray
  • Point of Intersection
  • Collinear Points
  • Coplanar Points
  • Coincident Lines
  • Collinear Line Segments and Rays
  • Transversal
  • Parallel Lines
  • Parallel Line Segments
  • Parallel Rays
  • Angle
  • Measure of Angle
  • Straight Angle
  • Supplementary Angles
  • Right Angle
  • Complementary Angles
  • Perpendicular Lines, Line Segments, and Rays
  • Triangle
  • Similar and Congruent Triangles
  • Direct Similarity
  • Inverse Similarity
  • Direct Congruence
  • Inverse Congruence
  • Two Crucial Facts
  • Two More Crucial Facts
  • Axioms
  • The Two-Point Axiom
  • The Extension Axiom
  • The Right Angle Axiom
  • The Parallel Axiom
  • The Side-Side-Side (SSS) Axiom
  • The Side-Angle-Side (SAS) Axiom
  • The Angle-Side-Angle (ASA) Axiom
  • The Side-Angle-Angle (SAA) Axiom
  • Some Proofs at Last
  • Alternate Interior Angles
  • Quiz
  • Chapter 5 Fallacies, Paradoxes, and Revelations
  • The Probability Fallacy
  • Belief
  • Parallel Worlds, Fuzzy Worlds
  • We Must Observe
  • Weak and Flawed Reasoning
  • "Proof" by Example
  • Begging the Question
  • Hasty Generalization
  • Misuse of Context
  • Circumstance
  • Fallacies with Syllogisms
  • Fun with Silliness
  • Inductive Reasoning
  • Simple Paradoxes
  • A Wire around the Earth
  • Direct-Contradiction Paradox
  • Who Shaves Hap?
  • Arrow Paradox
  • The Frog and the Wall
  • A Geometry Trick
  • A "proof" that – 1 = 1
  • Wheel Paradox
  • Classical Paradoxes
  • Execution Paradox
  • A Two-Pronged Defense
  • Saloon Paradox
  • Barbershop Paradox
  • Shark Paradox
  • Russell and Gödel
  • Sets
  • Two Special Sets
  • The Paradox
  • Professor N's Machine
  • What Did You Prove?
  • Quiz
  • Chapter 6 Strategies for Proofs
  • How Does a Theory Evolve?
  • Definitions
  • Elementary Terms
  • Axioms
  • Euclid's Postulates
  • A Denial
  • Propositions
  • Theorems
  • A Classical Theorem
  • Lemmas
  • Corollaries
  • Proofs, Truth, and Beauty
  • Techniques
  • Deductive Reasoning
  • What's the Universe?
  • Weak Theorems
  • Demonstrating a Weak Theorem
  • Strong Theorems
  • Demonstrating a Strong Theorem
  • Reductio ad Absurdum Revisited
  • Mathematical Induction
  • Cause, Effect, and Implication
  • Correlation and Causation
  • Complications
  • Quiz
  • Chapter 7 Boolean Algebra
  • New Symbols for Old Operations
  • The Not Operation (–)
  • The And Operation (X)
  • The Or Operation (+)
  • Boolean Implication ((omitted))
  • Boolean Equivalence (=)
  • Truth Tables, Boolean Style
  • Truth Table for Boolean Negation (NOT)
  • Truth Table for Boolean Multiplication (AND)
  • Truth Table for Boolean Addition (OR)
  • Truth Table for Boolean Implication (IF/THEN)
  • Truth Table for Boolean Equality (IFF)
  • Basic Boolean Laws
  • Precedence
  • Contradiction
  • Law of Double Negation
  • Commutative Laws
  • Associative Laws
  • Law of the Contrapositive
  • DeMorgan's Law for Products
  • DeMorgan's Law for Sums
  • Distributive Law
  • Quiz
  • Chapter 8 The Logic of Sets
  • Set Fundamentals
  • To Belong, or Not to Belong
  • Listing the Elements
  • The Empty Set
  • Finite or Infinite?
  • Sets within Sets
  • Venn Diagrams
  • People and Numbers
  • Subsets
  • Proper Subsets
  • Congruent Sets
  • Disjoint Sets
  • Overlapping Sets
  • Set Intersection
  • Intersection of Two Congruent Sets
  • Intersection with the Null Set
  • Intersection of Two Disjoint Sets
  • Intersection of Two Overlapping Sets
  • Set Union
  • Union of Two Congruent Sets
  • Union with the Null Set
  • Union of Two Disjoint Sets
  • Union of Two Overlapping Sets
  • Quiz
  • Chapter 9 The Logic of Machines
  • Numeration Systems
  • Decimal
  • Binary
  • Octal
  • Hexadecimal
  • Digital Circuits
  • Positive versus Negative Logic
  • Logic Gates
  • Black Boxes
  • Forms of Binary Data
  • Clocks
  • Counters
  • Digital Signals
  • Bits
  • Bytes
  • Baud
  • Examples of Data Speed
  • Analog-to-Digital Conversion
  • Digital-to-Analog Conversion
  • Serial versus Parallel
  • Digital Signal Processing
  • Digital Color
  • Quiz
  • Chapter 10 Reality Remystified
  • The Illogic of Time
  • The Light-Beam Conundrum
  • Synchronize Your Watches!
  • When Is a Second Not a Second?
  • Traveling into the Future
  • Traveling into the Past
  • The Twin Paradox
  • The Illogic of Matter and Space
  • Particles without End
  • A Mad Professor's Monologue
  • Order from Randomness
  • The Ultimate State of Order
  • Hyperspace
  • Hypospace
  • Time-Space
  • Time as a Dimension
  • Infinity-Space
  • The Dwindling-Displacement Effect
  • The Illogic of Chaos
  • Was Andrew "Due"?
  • Slumps and Spurts
  • Correlation, Coincidence, or Chaos?
  • Scale-Recurrent Patterns
  • The Maximum Unswimmable Time
  • The Butterfly Effect
  • Scale Parallels
  • The Malthusian Model
  • A Bumpy Ride
  • What Is Randomness?
  • Final Exam
  • Answers to Quizzes and Final Exam
  • Suggested Additional Reading
  • Index