reface Chapter 1: Introductory Concepts 1.1 - Critical Thinking, Logic and Arguments 1 Arguments 1 Statements 1 Premises and Conclusions 2 Inference 3 Identifying Arguments 5 Evaluating Arguments 6 Exercises 10 Chapter 2: Categorical Logic 2.1 - Introduction 13 Exercises 14 2.2 - Diagramming Categorical Statements 14 The Four Categorical Statement Forms 16 Venn Diagrams for Categorical Statements 18 Exercises 24 2.3 - Operations on Categorical Statements 26 Conversion 26 Obversion 29 Contraposition 34 Table of Operations on Categorical Statements 38 Exercises 39 2.4 - Categorical Arguments 40 Three-circle Venn Diagrams 41 Diagramming Arguments 43 Evaluating Arguments using Venn Diagrams 47 Exercises 55 2.5 - Applications of Categorical Logic 59 General Rules for Categorical Syllogisms 59 Enthymemes 59 Exercises 64 Sorites 66 Exercises 69 Chapter 3: Sentential/Propositional Logic 3.1 - Introduction 71 3.2 - Simple Statements 71 3.3 - Operators 72 Negation 72 Conjunction 73 Disjunction 74 Conditional 74 3.4 - Symbolizing Compound Statements 74 Exercises 78 3.6 - Truth Values 80 3.7 - Truth Tables 80 Characteristic Truth Table for the Negation 81 Characteristic Truth Table for the Conjunction 83 Characteristic Truth Table for the Disjunction 85 Characteristic Truth Table for the Conditional 86 Summary of Characteristic Truth Tables 88 3.8 - Partial Truth Tables for Compound Statements 90 Exercises 93 3.9 - Complete Truth Tables 95 Truth Table Patterns for Single Statements 100 Exercises 101 Truth Table Patterns for Sets of Statements 101 Exercises 104 3.10 - Shortened Truth Tables for Consistency and Validity 105 Exercises 111 3.11 - The Indirect Method for Consistency and Validity 112 Exercises 122 Chapter 4: The Natural System of Deduction 4.1 - Introduction 124 4.2 - The Rules of Inference 124 Conjunction Elimination (&E) 124 Disjunctive Syllogism (DS) 125 4.3 - Introduction to Derivations 126 Deriving Compound Statements 129 Exercises 130 4.4 - More Derivation Rules 131 Conjunction Introduction (&I) 131 Modus Ponens (MP) 131 Modus Tollens (MT) 131 Two Common Conditional Derivation Errors 132 Disjunction Introduction ( I) 133 4.5 - More Derivation Practice 134 Building statements in proofs 137 Exercises 139 4.6 - The Rules of Replacement 141 Double Negation Elimination (~~E) 141 Commutation (Comm) 141 Association (Ass) 141 DeMorgan's Rules (DeM) 142 Negated Conditional Replacement (NCR) 143 4.6 - Some Common Derivation Strategies 143 Wedge Introduction 1