Logic for Physicists

Contents 1 Dedication 2 Introduction 3 Mathematical Logic 4 Propositional Algebra 4.1 Propositions 4.1.1 What is a Proposition? 4.1.2 Law of Dichotomy 4.1.3 Law of the Excluded Middle 4.1.4 Proposition vs. Statements 4.1.5 Equal Propositions 4.1.6 Examples 4.2 Logical Operators 4.2.1 What is a Logical Operator? 4.2.2 The ⊗ Operator (BOTH-FALSE) 4.2.3 The ¬ Operator (NOT) 4.2.4 The ∨ Operator (OR) 4.2.5 The ∧ Operator (AND) 4.2.6 The =⇒ Operator (IMPLIES) 4.2.7 The ⇐⇒ Operator (EQUIVALENT) 4.3 Notes on Notation 4.4 The T and F Symbols 4.5 Properties of Logical Operators ¬, ∨, and ∧ 4.5.1 Properties of ⊗ (BOTH-FALSE) 4.5.2 Properties of ¬ (NOT) 4.5.3 Properties of ∨ (OR) 4.5.4 Properties of ∧ (AND) 4.5.5 Mixed Properties of ¬, ∨, and ∧ 4.5.6 Additional Mixed Properties of ¬, ∨, and ∧ 4.5.7 Properties of =⇒ (IMPLIES) 4.6 The ⊢ Symbol 4.6.1 What is the ⊢ Symbol? 4.6.2 General Properties of ⊢ 4.6.3 A Fundamental Property of ⊢ 4.6.4 An Example 4.6.5 Additional Properties of ⊢ 5 Predicate Logic 5.1 What is Predicate Logic? 5.2 The ∀ Symbol (FOR ALL) 5.3 The ∃ Symbol (EXISTS) 5.4 Properties of the Logical Symbols ∀ and ∃ 6 Deductive Reasoning 6.1 What is Deductive Reasoning? 6.2 An Example 7 Appendix 7.1 Truth Tables of Logical Operators 7.2 General Equations of Propositional Algebra 7.2.1 Properties of ⊗ 7.2.2 Properties of ¬, ∨, and ∧ 7.2.3 Properties of =⇒ 7.2.4 Properties of ⊢ 7.3 General Equations of Predicate Logic