Gain insights into fundamental set theory concepts and operations. Explore relations, functions, set ordering, and cardinality using Python. Delve into Cantor’s diagonalization and its applications in various fields.

This course aims to introduce fundamental concepts of set theory. It provides hands-on experience through practical tasks using Python programming language (Python 3.8) to enhance engagement.

You’ll start with the basics of sets, their properties, and set operations. Additionally, you’ll learn about relations, functions, ordering of sets, and cardinality of sets. You’ll also explore Cantor’s diagonalization method as a tool to demonstrate the uncountability of sets. 

After completing this course, you’ll have a solid understanding of the foundations of set theory that are vital for understanding many mathematics and computer science concepts, such as discrete mathematics, design of algorithms, theory of automata, and problem-solving. These concepts can also be applied in other significant areas including Physics, Statistics, and Probability.

An Introduction to Basic Set Theory

The **logical AND** is a binary operation represented by the symbol $\land$. When two propositions are connected using the logical AND operation, it becomes a new proposition whose value depends on the truth values of the operands. Let’s have a look at the values of a proposition formed from two other propositions, $p$ and $q$, using the AND operator. In the following table, called the truth table, we represent true by "T" and false by "F": 

Brush up the background concepts required for this course including propositions and the logical AND, OR, and NOT operations.

Introduction

Fundamentals

Basic Set Operations

Assessment 1

Relations

Assessment 2

Functions

Assessment 3

Indexing and Ordering of Sets

Cardinality of Sets

Assessment 4

Concluding Remarks

Appendix

Proposition

The logical AND operation