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.

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