Logic DeMYSTiFied

## Making sense of LOGIC just got a whole lot EASIER! Stumped trying to understand logic? It's time to listen to reason! There's no doubt that __Logic Demystified__ will help you master this challenging subject. Written in a step-by-step format, this practical guide begins by covering arguments, validity, and truth tables. You'll move on to propositional and predicate logic, rigor, fallacies, paradoxes, and revelations. Proofs, Boolean algebra, the logic of machines, and sets are discussed as is the illogic of time, matter, space, and chaos. Detailed examples and concise explanations make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning. **It's a no-brainer! You'll get:*** Rules for reasoning * Quantified statements and theorems * Simple and classical paradoxes * Strategies for proofs * Basic set theory and machine logic * A time-saving approach to performing better on homework, an exam, or at work __Simple enough for a beginner, but challenging enough for an advanced student, **Logic Demystified** helps you validate your knowledge of this multidisciplinary topic.__ Contents 8 Preface 18 Chapter 1 Arguments, Validity, and Truth Tables 22 What's Logic About? 23 Terminology 23 Logical Arguments 23 What's Logic Good For? 24 Logical Form 24 An Example 25 When Truth Doesn't Matter 25 When Meaning Doesn't Matter 25 Rules for Reasoning 26 Identity 26 Contradiction 27 True or False 27 Sentence Forms 27 Subject/Verb (SV) Statements 27 Subject/Verb/Object (SVO) Statements 28 Subject/Linking Verb/Complement (SLVC) Statements 28 Symbols and Operations 29 Logical Negation (NOT) 29 Logical Conjunction (AND) 30 Inclusive Logical Disjunction (OR) 30 Exclusive Logical Disjunction (XOR) 31 Logical Implication (IF/THEN) 32 Logical Equivalence (IFF) 33 Tables for Basic Operations 35 Table for Logical Negation 35 Table for Conjunction 35 Tables for Logical Disjunction 36 Table for Logical Implication 36 Table for Logical Equivalence 37 A Quick Proof 38 Precedence 39 Examples of Precedence 40 Proofs Using Truth Tables 41 Reversing the Order of a Conjunction 42 Grouping of Conjunctions 42 Reversing the Order of an Inclusive Disjunction 44 Grouping of Inclusive Disjunctions 44 Reversing the Order of an Implication 46 Ungrouping the Negation of a Conjunction 46 Ungrouping the Negation of an Inclusive Disjunction 47 Regrouping with Mixed Operations 48 Truth Tables Have Power! 48 Quiz 52 Chapter 2 Propositional Logic 54 A Formal System 55 Propositional Formulas (PFs) 55 Is This Mathematics? 56 Contradiction 56 Sequents 57 Backing Up the Argument 58 Assumption (A) 58 Double Negation (DN) 59 Conjunction Introduction (ΛI) 60 Conjunction Elimination (ΛE) 60 Disjunction Introduction ((omitted)I) 61 Disjunction Elimination ((omitted)E) 61 Conditional Proof (CP) and Theorems 63 Biconditional Introduction ((omitted)I) 65 Biconditional Elimination ((omitted)E) 66 Substitution 66 Laws 69 Law of Contradiction 69 Law of Excluded Middle 69 Law of Double Negation 70 Commutative Laws 70 Associative Laws 71 Law of Implication Reversal 72 DeMorgan's Laws 74 Distributive Laws 75 Interderivability ((omitted)), Deriving Laws, and Theorem Introduction (TI) 75 Quiz 78 Chapter 3 Predicate Logic 82 Symbolizing Sentence Structure 83 Formal Predicates 83 Formal Subjects: Names 83 Formal Subjects: Variables 83 Predicate Sentence Formulas 84 More Predicate Sentences 85 Identity (=) 86 Building More Complex Formulas 86 Quantified Statements 87 Some versus All 87 The Existential Quantifier ((omitted)) 88 The Universal Quantifier ((omitted)) 89 The Universe 89 Multiple Quantifiers 91 Translating the Quantifiers 93 Laws of Quantifier Transformation 93 Logical Relationships: The Square of Opposition 94 Well-Formed Formulas 95 Properties of Two-Part Relations 96 Symmetry 96 Asymmetry 97 Antisymmetry 97 Nonsymmetry 97 Reflexivity 98 Irreflexivity 98 Nonreflexivity 98 Transitivity 98 Intratransitivity 99 Nontransitivity 99 Equivalence Relations 99 Predicate Proofs 99 Existential Introduction ((omitted)I) 100 Existential Elimination ((omitted)E) 100 Universal Introduction ((omitted)I) 101 Universal Elimination ((omitted)E) 102 Identity Introduction (=I) 102 Identity Elimination (=E) 103 Conventions for Predicate Proofs 103 Syllogisms 107 A Sample Syllogism 108 Allowed Propositions 108 Terms and Arguments 109 Conversion Laws 110 Classifying Syllogisms: Mood and Figure 110 Testing Syllogistic Arguments 111 Valid Syllogisms 114 Other Kinds of Syllogism 114 Quiz 116 Chapter 4 A Boot Camp for Rigor 120 Definitions 121 Elementary Terms 121 Line Segment 121 Half-Open Line Segment 122 Open Line Segment 122 Length of Line Segment 123 Closed-Ended Ray 123 Open-Ended Ray 123 Point of Intersection 123 Collinear Points 124 Coplanar Points 124 Coincident Lines 124 Collinear Line Segments and Rays 124 Transversal 125 Parallel Lines 125 Parallel Line Segments 125 Parallel Rays 125 Angle 127 Measure of Angle 129 Straight Angle 129 Supplementary Angles 130 Right Angle 130 Complementary Angles 130 Perpendicular Lines, Line Segments, and Rays 130 Triangle 131 Similar and Congruent Triangles 133 Direct Similarity 133 Inverse Similarity 134 Direct Congruence 136 Inverse Congruence 138 Two Crucial Facts 139 Two More Crucial Facts 140 Axioms 141 The Two-Point Axiom 141 The Extension Axiom 141 The Right Angle Axiom 141 The Parallel Axiom 142 The Side-Side-Side (SSS) Axiom 142 The Side-Angle-Side (SAS) Axiom 143 The Angle-Side-Angle (ASA) Axiom 144 The Side-Angle-Angle (SAA) Axiom 144 Some Proofs at Last 146 Alternate Interior Angles 151 Quiz 163 Chapter 5 Fallacies, Paradoxes, and Revelations 166 The Probability Fallacy 167 Belief 167 Parallel Worlds, Fuzzy Worlds 167 We Must Observe 168 Weak and Flawed Reasoning 169 "Proof" by Example 169 Begging the Question 171 Hasty Generalization 172 Misuse of Context 172 Circumstance 172 Fallacies with Syllogisms 173 Fun with Silliness 175 Inductive Reasoning 176 Simple Paradoxes 179 A Wire around the Earth 179 Direct-Contradiction Paradox 181 Who Shaves Hap? 182 Arrow Paradox 182 The Frog and the Wall 183 A Geometry Trick 186 A "proof" that – 1 = 1 188 Wheel Paradox 190 Classical Paradoxes 191 Execution Paradox 191 A Two-Pronged Defense 192 Saloon Paradox 193 Barbershop Paradox 194 Shark Paradox 195 Russell and Gödel 196 Sets 196 Two Special Sets 196 The Paradox 197 Professor N's Machine 198 What Did You Prove? 199 Quiz 200 Chapter 6 Strategies for Proofs 202 How Does a Theory Evolve? 203 Definitions 203 Elementary Terms 204 Axioms 205 Euclid's Postulates 205 A Denial 207 Propositions 208 Theorems 208 A Classical Theorem 209 Lemmas 210 Corollaries 210 Proofs, Truth, and Beauty 213 Techniques 215 Deductive Reasoning 215 What's the Universe? 216 Weak Theorems 217 Demonstrating a Weak Theorem 217 Strong Theorems 218 Demonstrating a Strong Theorem 219 Reductio ad Absurdum Revisited 220 Mathematical Induction 222 Cause, Effect, and Implication 226 Correlation and Causation 226 Complications 229 Quiz 233 Chapter 7 Boolean Algebra 236 New Symbols for Old Operations 237 The Not Operation (–) 237 The And Operation (X) 237 The Or Operation (+) 238 Boolean Implication ((omitted)) 239 Boolean Equivalence (=) 240 Truth Tables, Boolean Style 241 Truth Table for Boolean Negation (NOT) 242 Truth Table for Boolean Multiplication (AND) 242 Truth Table for Boolean Addition (OR) 242 Truth Table for Boolean Implication (IF/THEN) 243 Truth Table for Boolean Equality (IFF) 243 Basic Boolean Laws 248 Precedence 248 Contradiction 249 Law of Double Negation 249 Commutative Laws 249 Associative Laws 250 Law of the Contrapositive 250 DeMorgan's Law for Products 251 DeMorgan's Law for Sums 251 Distributive Law 251 Quiz 257 Chapter 8 The Logic of Sets 260 Set Fundamentals 261 To Belong, or Not to Belong 261 Listing the Elements 261 The Empty Set 262 Finite or Infinite? 262 Sets within Sets 263 Venn Diagrams 265 People and Numbers 265 Subsets 266 Proper Subsets 266 Congruent Sets 267 Disjoint Sets 268 Overlapping Sets 269 Set Intersection 274 Intersection of Two Congruent Sets 274 Intersection with the Null Set 274 Intersection of Two Disjoint Sets 274 Intersection of Two Overlapping Sets 275 Set Union 277 Union of Two Congruent Sets 278 Union with the Null Set 278 Union of Two Disjoint Sets 278 Union of Two Overlapping Sets 279 Quiz 284 Chapter 9 The Logic of Machines 286 Numeration Systems 287 Decimal 288 Binary 288 Octal 289 Hexadecimal 289 Digital Circuits 295 Positive versus Negative Logic 295 Logic Gates 296 Black Boxes 297 Forms of Binary Data 298 Clocks 299 Counters 299 Digital Signals 302 Bits 302 Bytes 303 Baud 303 Examples of Data Speed 304 Analog-to-Digital Conversion 304 Digital-to-Analog Conversion 306 Serial versus Parallel 306 Digital Signal Processing 307 Digital Color 307 Quiz 313 Chapter 10 Reality Remystified 318 The Illogic of Time 319 The Light-Beam Conundrum 319 Synchronize Your Watches! 320 When Is a Second Not a Second? 321 Traveling into the Future 324 Traveling into the Past 325 The Twin Paradox 325 The Illogic of Matter and Space 329 Particles without End 329 A Mad Professor's Monologue 330 Order from Randomness 331 The Ultimate State of Order 332 Hyperspace 333 Hypospace 334 Time-Space 335 Time as a Dimension 335 Infinity-Space 337 The Dwindling-Displacement Effect 338 The Illogic of Chaos 340 Was Andrew "Due"? 340 Slumps and Spurts 340 Correlation, Coincidence, or Chaos? 341 Scale-Recurrent Patterns 342 The Maximum Unswimmable Time 343 The Butterfly Effect 344 Scale Parallels 345 The Malthusian Model 346 A Bumpy Ride 347 What Is Randomness? 350 Final Exam 352 Answers to Quizzes and Final Exam 384 Suggested Additional Reading 386 Index 388 A 388 B 388 C 389 D 389 E 390 F 390 G 390 H 391 I 391 K 391 L 391 M 392 N 392 O 393 P 393 Q 394 R 394 S 394 T 395 U 396 V 396 W 396 XYZ 396

Making sense of LOGIC just got a whole lot EASIER!

Stumped trying to understand logic? It's time to listen to reason! There's no doubt that Logic Demystified will help you master this challenging subject.

Written in a step-by-step format, this practical guide begins by covering arguments, validity, and truth tables. You'll move on to propositional and predicate logic, rigor, fallacies, paradoxes, and revelations. Proofs, Boolean algebra, the logic of machines, and sets are discussed as is the illogic of time, matter, space, and chaos. Detailed examples and concise explanations make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning.

It's a no-brainer! You'll get:

• Rules for reasoning
• Quantified statements and theorems
• Simple and classical paradoxes
• Strategies for proofs
• Basic set theory and machine logic
• A time-saving approach to performing better on homework, an exam, or at work

Simple enough for a beginner, but challenging enough for an advanced student, Logic Demystified helps you validate your knowledge of this multidisciplinary topic.

"Making sense of LOGIC just got a whole lot EASIER!Stumped trying to understand logic? It's time to listen to reason! There's no doubt that Logic Demystified will help you master this challenging subject. Written in a step-by-step format, this practical guide begins by covering arguments, validity, and truth tables. You'll move on to propositional and predicate logic, rigor, fallacies, paradoxes, and revelations. Proofs, Boolean algebra, the logic of machines, and sets are discussed as is the illogic of time, matter, space, and chaos. Detailed examples and concise explanations make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning. It's a no-brainer! You'll get: *Rules for reasoning *Quantified statements and theorems *Simple and classical paradoxes *Strategies for proofs *Basic set theory and machine logic *A time-saving approach to performing better on homework, an exam, or at workSimple enough for a beginner, but challenging enough for an advanced student, Logic Demystified helps you validate your knowledge of this multidisciplinary topic."-- Provided by publisher Written in a step-by-step format, this practical guide begins by covering arguments, validity, and truth tables. Then you move on to propositional and predicate logic, rigor, fallacies, paradoxes, and revelations, then proofs, boolean algebra, the logic of machines and sets are discussed as is the illogic of time, matter, space and chaos