Important Terms Related to Set Theory
Some of the important terms related to sets are mentioned below. These terms will be used several times in this article, and knowing these terms will help you learn set theory.
Elements of a Set
The objects contained by a set are called the elements of the set.
They are represented using the ∈ symbol which means “belongs to”.
For Example:
In the set of Natural Numbers, 1, 2, 3, etc. are the objects, hence they are the elements of the set of Natural Numbers.
We can also say that 1 belongs to set N and it is represented as 1 ∈ N.
Cardinal Number of a Set
The number of elements present in a set is called the Cardinal Number of a Set.
For Example:
Suppose P is a set of the first five prime numbers given by P = {2, 3, 5, 7, 11}, then the Cardinal Number of set P is 5.
The Cardinal Number of Set P is represented by n(P) or |P| = 5.
What is Set Theory? Definition, Types, Operations
Set Theory is a branch of logical mathematics that studies the collection of objects and operations based on it. A set is simply a collection of objects or a group of objects. For example, a group of players in a football team is a set and the players in the team are its objects.
The words collection, aggregate, and class are synonymous with set. On the other hand elements, members, and objects are synonymous and stand for the members of the set of which the set is comprised.
In this article, we will learn about the set theory and cover sets in detail. Look at the content guide that shows all the topics, we will be covering in this article.
Table of Content
- Set Theory Definition
- History of Set Theory
- Examples of Sets
- Important Terms Related to Set Theory
- Elements of a Set
- Cardinal Number of a Set
- Representation of Sets
- Roster Form
- Set Builder Form
- Types of Sets
- Set Theory Symbols
- Set Theory Operations
- Properties of Set Operations
- Set Theory Formulas
- De Morgan’s Laws
- De Morgan’s Law of Union
- De Morgan’s Law of Intersection
- Visual Representation of Sets Using Venn Diagram
- Solved Examples on Set Theory
- Practice Problems on Set Theory