Logic Demystified

Logic DeMYS TiFieD anthony Boutelle Stan Gibilisco Copyright © 2011 by The McGraw-Hill Companies, Inc. ISBN: 978-0-07-170129-7 MHID: 0-07-170129-X The material in this eBook also appears in the print version of this title: ISBN: 978-0-07-170128-0, MHID: 0-07-170128-1. Contents Preface chapter 1 Arguments, Validity, and Truth Tables xvii 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 chapter 2 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 14 14 14 15 15 16 17 18 19 20 21 21 23 23 25 25 Propositional Logic 33 A Formal System Propositional Formulas (PFs) Is This Mathematics? Contradiction Sequents Backing Up the Argument Assumption (A) Double Negation (DN) Conjunction Introduction (ŸI) Conjunction Elimination (ŸE) Disjunction Introduction (⁄I) Disjunction Elimination (⁄E) Conditional Proof (CP) and Theorems Biconditional Introduction (´I) Biconditional Elimination (´E) Substitution Laws Law of Contradiction Law of Excluded Middle 26 27 27 31 34 34 35 35 36 37 37 38 39 39 40 40 42 44 45 45 48 48 48 chapter 3 Law of Double Negation Commutative Laws Associative Laws Law of Implication Reversal DeMorgan’s Laws Distributive Laws Interderivability ( ), Deriving Laws, and   Theorem Introduction (TI) Quiz 54 57 Predicate Logic 61 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 ($) The Universal Quantifier (") The Universe Multiple Quantifiers Translating the Quantifiers Laws of Quantifier Transformation Logical Relationships: The Square   of Opposition Well-Formed Formulas Properties of Two-Part Relations Symmetry Asymmetry Antisymmetry Nonsymmetry Reflexivity Irreflexivity Nonreflexivity Transitivity Intratransitivity Nontransitivity Equivalence Relations 49 49 50 51 53 54 62 62 62 62 63 64 65 65 66 66 67 68 68 70 72 72 73 74 75 75 76 76 76 77 77 77 77 78 78 78 chapter 4 Predicate Proofs Existential Introduction ($I) Existential Elimination ($E) Universal Introduction ("I) Universal Elimination ("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 78 79 79 80 81 81 82 82 86 87 87 88 89 89 90 93 93 95 A Boot Camp for Rigor 99 Definitions Elementary Terms Line Segment Half-Open Line Segmen