Concise Introduction to Logic and Set Theory (Mathematics and its Applications)

✍ Scribed by Iqbal H. Jebril, Hemen Dutta, Ilwoo Cho

• Publisher: CRC Press
• Year: 2021
• Tongue: English
• Leaves: 171
• Edition: 1
• Category: Library

✦ Synopsis

This book deals with two important branches of mathematics, namely, logic and set theory. Logic and set theory are closely related and play very crucial roles in the foundation of mathematics, and together produce several results in all of mathematics.

The topics of logic and set theory are required in many areas of physical sciences, engineering, and technology. The book offers solved examples and exercises, and provides reasonable details to each topic discussed, for easy understanding.

The book is designed for readers from various disciplines where mathematical logic and set theory play a crucial role. The book will be of interested to students and instructors in engineering, mathematics, computer science, and technology.

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Contents
Preface
About Authors
Chapter 1: Mathematical Logic
1.1. Sets
1.2. Propositions and Connectives
1.3. Tautology and Contradiction
1.4. Quantifiers
1.5. Logical Reasoning
1.6. Mathematical Proof
1.6.1. Direct and contrapositive Proof
1.6.2. Contradiction Proof
1.7. Induction
1.7.1. Introduction
1.7.2. Induction Principle
Chapter 2: Set Theory
2.1. Basic Notions of Set Theory
2.2. Elementary Properties of Sets
2.2.1. Union of Sets
2.2.2. Intersection of Sets
2.2.3. Complement of Set
2.2.4. Difference and Symmetric Difference of Sets
2.3. Indexed Families of Sets
Chapter 3: Relations
3.1. Ordered Pairs and Cartesian Product
3.2. Relations on Sets
3.3. Type of Relations
3.4. Equivalence Relations and Equivalence Classes
3.5. Congruence
3.6. Partial and Total Ordered Relations
Chapter 4: Functions
4.1. Functions
4.1.1. Domain and Range
4.1.2. Graph of a Function
4.2. One-to-one Functions and Onto Functions
4.3. Composite Functions and Inverse Functions
4.4. Direct Images and Inverse Images under a Function
Chapter 5: Cardinality of Sets
5.1. Cardinal Number
5.1.1. Equipotent Sets
5.1.2. Countable Sets
5.1.3. Cardinal Arithmetic
5.1.4. Order Types
5.1.5. More About Cardinal Numbers
5.2. Axiom of Choice
Bibliography
Index