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

• 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.

Foundations

The basics explained with examples and symbols.

• Sets in Maths
• Representation of Sets
• Types of Sets

Set Relationships

This section explains how sets relate to one another.

• Subsets
• Supersets
• Power Set
• Quick References: Set Theory Symbols | Set Notations in LaTeX

Operations & Visualization

Combining, comparing, and visualizing sets

• Venn Diagrams
• Operations on Sets
• Cardinality of Sets
• De Morgan's Laws
• Set Theory Formulas
• Cartesian Product of a Set

Practice

Solved questions, quizzes, and practice problems to test your understanding.

• Set Theory Solved Questions
• Set Theory - Quiz
• Practice Operation on Set

Programs of Set Theory

How sets work in C++, Python, C#, and JavaScript using built-in set data structures.

• 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

Common set-based DSA problems: unions, intersections, duplicates, and more.

• 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