Set theory is a branch of mathematics that deals with collections of objects, called sets. A set is simply a collection of distinct elements, such as numbers, letters, or even everyday objects, that share a common property or rule.
Some examples of sets include:
A set of fruits: {apple, banana, orange}A set of numbers: {1, 2, 3, 4}A set of even numbers: {2, 4, 6, 8, 10, …}A set of months with exactly 6 Sundays: {∅}. This set is empty, as no month has exactly 6 Sundays.
- A set of fruits: {apple, banana, orange}
- A set of numbers: {1, 2, 3, 4}
- A set of even numbers: {2, 4, 6, 8, 10, …}
- A set of months with exactly 6 Sundays: {∅}. This set is empty, as no month has exactly 6 Sundays.
{apple, banana, orange}
{1, 2, 3, 4}
A set of even numbers: {2, 4, 6, 8, 10, ....}
This section introduces the basics of Set Theory, helping you understand key concepts like types of sets, set operations, and important formulas through clear examples and symbols.
- Sets in Maths
- Representation of Sets: [ Roaster Form] and [ Set Builder Notation ]
- Subsets
- Supersets
- Power Set
- Set Theory Symbols
- Set Theory Formulas
- Types of Sets
- Operations on Sets
- Cardinality of Sets
- Venn Diagrams
- De Morgan’s Laws
- Set Notations in LaTeX
This part covers advanced Set Theory concepts like Cartesian products, relations, and functions, helping you learn how sets connect and interact in more complex ways.
- Cartesian Product of a Set
- Relation
- Functions: [ Types of Functions ]
This section offers solved questions, quizzes, and practice problems to help you strengthen your understanding of Set Theory and master set operations.
- Set Theory Solved Questions
- Set Theory - Quiz
- Practice Operation on Set
This section shows how to work with sets in different programming languages like C++, Python, C#, and JavaScript, using built-in set data structures and operations.
- Set in C++
- Unordered Set in C++
- Multiset in C++
- Set in Python
- Set in C#
- Set in JavaScript
This section covers common set-based problems in data structures, helping you solve tasks like finding unions, intersections, removing duplicates, and more using sets.
- Find the Union and Intersection of two unsorted arrays
- Count distinct elements in an array
- Longest Consecutive Subsequence
- Remove duplicates from a sorted array
- K’th Smallest/Largest Element in Unsorted Array
Set Theory is the study of a collection of objects which are called sets and the relation between different sets.
Set Theory is the study of a collection of objects which are called sets and the relation between different sets.
Set is a well-defined collection of objects. These objects are called the element of sets.
Set is a well-defined collection of objects. These objects are called the element of sets.
Set Theory was invented by German Mathematician Georg Cantor.
Set Theory was invented by German Mathematician Georg Cantor.
Algebra of Sets deals with the following laws:Commutative LawsAssociative LawDistributive LawIdentity LawIdempotent LawThese laws are covered in the article under Properties of Sets.
Algebra of Sets deals with the following laws:
- Commutative Laws
- Associative Law
- Distributive Law
- Identity Law
- Idempotent Law
These laws are covered in the article under Properties of Sets.
A subset is a set that has fewer or equal elements of another set. The other set is called a Superset.
A subset is a set that has fewer or equal elements of another set. The other set is called a Superset.
De Morgan’s Law is a law that deals with the union and intersection of sets with the intersection and union of individual sets respectively. There are two laws under it namely De Morgan’s Law of Union and De Morgan’s Law of Intersection. These are covered under the section of De Morgan’s Law in this article.
De Morgan’s Law is a law that deals with the union and intersection of sets with the intersection and union of individual sets respectively. There are two laws under it namely De Morgan’s Law of Union and De Morgan’s Law of Intersection. These are covered under the section of De Morgan’s Law in this article.