Set Theory

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.

Example of Sets

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.

Key Concepts in Set Theory

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

Advanced Topics of Set Theory

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 ]

Practice for Set Theory

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

Programs of Set Theory

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

Standard Problems Associated with Set Data Structure

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

Commonly Asked Questions on Set Theory

What is the basis of set theory?

Set Theory is the study of a collection of objects which are called sets and the relation between different sets.

How do you define a set?

Set is a well-defined collection of objects. These objects are called the element of sets.

Who Invented Set Theory?

Set Theory was invented by German Mathematician Georg Cantor.

What is the Algebra 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.

What is a Subset?

A subset is a set that has fewer or equal elements of another set. The other set is called a Superset.

What is De Morgan's Law?

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.