# Logic for Physicists

- Nicolas A Pereyra

- June 2018

### Description

This book gives a rigorous yet physics focused introduction to mathematical logic that is geared towards natural science majors. We present the science major with a robust introduction to logic, focusing on the specific knowledge and skills that will unavoidably be needed in calculus topics, and natural science topics in general, rather than taking a philosophical-math-fundamental oriented approach that is commonly found in mathematical logic textbooks.### About Editors

Dr Pereyra graduated with an undergraduate degree in physics from the Universidad Central De Venezuela in 1991. He then studied at University of Maryland at College Park, where he obtained his MS in 1995 and his PhD in 1997. He is currently an associate professor in astrophysics at the Physics and Astronomy Department of the University of Texas Rio Grande Valley. Dr Pereyra's research work has been largely in the development of computational models of physical systems.### Table of Contents

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

### Bibliographic

Paperback ISBN: 9780750329200

Ebook ISBN: 9781643270159

DOI: 10.1088/978-1-6432-7016-6

Publisher: Morgan & Claypool Publishers