Counting Of Relations in Group Theory | Lecture 02 (I) by Dubey Sir | CSIR NET | IIT JAM | GATE Math

In this lecture, Dubey Sir explores the concept of Counting Relations in the context of Group Theory. As part of the Group Theory series, this session focuses on understanding how relations are defined between sets and the different ways to count these relations systematically.

Key topics covered in the lecture include:
• Definition of relations between two sets and their role in algebraic structures.
• Introduction to different types of relations such as reflexive, symmetric, and transitive.
• Counting relations: Sir explains the process of determining the number of possible relations between two sets.
• Examples of counting relations between sets of different sizes, providing practical applications and clarity on the topic.

This lecture serves as a foundational part of understanding more advanced concepts in Group Theory and Algebra, making it especially useful for students preparing for competitive exams like CSIR NET, GATE, and IIT JAM.

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𝗟𝗲𝗰𝘁𝘂𝗿𝗲: 02 (Part 01)

00:44 INTRODUCTION
08:09 COUNTING OF RELATION
08:57 COUNTING OF REFLEXIVE RELATION
10:38 NO. OF IRREFLEXIVE RELATION
11:11 NO. OF SYMMETRIC RELATION
16:17 QUESTION
23:27 NO. OF ASYMMETRIC RELATION
26:11 NO. OF ANTISYMMETRIC RELATION
27:08 EXAMPLE
30:00 EXAMPLE
36:00 EXAMPLE

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This video is about;
How do you count relations in a set?
How do you count the number of relations?
How to count the number of reflexive relations?
How do we find the number of irreflexive relations?
What is the formula for the number of symmetric and reflexive relations?
How do you find the number of antisymmetric relations?
How do you count the number of binary relations?
What is the total number of reflexive relations?
What is reflexive relation with example?
How to know if a relation is reflexive?
What is the difference between reflexive and irreflexive relationships?
Counting Transitive Relations
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