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

# Intersection
A **set intersection** is a binary operation, which means two sets are required to perform this operation. The intersection of sets $A$ and $B$ is set $C$, which contains every element that is a member of both $A$ and $B$.
 We can write this definition as follows:

$$C=A \cap B = \{x \mid x\in A \land x\in B\}$$

If an object is a member of both $A$ and $B$, it will appear in $C$. 

 
The following facts are obvious from the definition of the intersection operation, where $\mathbb{U}$ is the universal set, $A$ is an arbitrary set, and $\emptyset$ is the empty set:

$$A\cap \emptyset = \emptyset \cap A = \emptyset \\A\cap \mathbb{U} = \mathbb{U} \cap A = A$$



## Cardinality 
Further, if $C=A∩B$, where $A$ and $B$ are finite sets, the cardinality of $C$ cannot be greater than the cardinality of $A$ or $B$—that is, $|C|\le |A|$ and $|C|\le |B|$.




Learn about the intersection operations defined for sets.

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

Intersection