Mathematics Exam > Mathematics Videos > Mathematics for IIT JAM, GATE, CSIR NET, UGC NET > Equivalence relation
Equivalence relation Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
|
556 videos|198 docs
|
FAQs on Equivalence relation Video Lecture - Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
| 1. What is an equivalence relation? |  |
Ans. An equivalence relation is a relation that is reflexive, symmetric, and transitive. In other words, it is a relation that satisfies three properties: every element is related to itself (reflexive property), if element A is related to element B, then element B is also related to element A (symmetric property), and if element A is related to element B and element B is related to element C, then element A is also related to element C (transitive property).
| 2. How do you determine if a relation is an equivalence relation? | |
Ans. To determine if a relation is an equivalence relation, you need to check if it satisfies three properties: reflexivity, symmetry, and transitivity. If for every element in the set, it is related to itself (reflexivity), for every pair of related elements, the reverse relation also holds (symmetry), and for any three related elements, the first element is also related to the third element (transitivity), then the relation is an equivalence relation.
| 3. Can you provide an example of an equivalence relation? | |
Ans. Yes, one example of an equivalence relation is the relation of equality on the set of integers. In this relation, any integer is related to itself (reflexivity), if two integers are equal, then they are related to each other (symmetry), and if two integers are equal and a third integer is also equal to the second integer, then the first integer is also equal to the third integer (transitivity).
| 4. What are the applications of equivalence relations in mathematics? | |
Ans. Equivalence relations have various applications in mathematics. They are used in algebraic structures, such as groups and rings, to define equivalence classes and quotient structures. Equivalence relations also play a crucial role in set theory, where they are used to partition sets into disjoint subsets. Additionally, equivalence relations are utilized in graph theory to study connectedness and in topology to define homeomorphism between spaces.
| 5. How are equivalence relations related to partitions? | |
Ans. Equivalence relations and partitions are closely related concepts. An equivalence relation on a set divides the set into disjoint subsets called equivalence classes. These equivalence classes form a partition of the set, where each element belongs to exactly one equivalence class. Conversely, any partition of a set defines an equivalence relation, where two elements are related if and only if they belong to the same subset in the partition. Thus, equivalence relations and partitions provide alternative ways to describe the same underlying structure.
Related Exams
About this Video
|
4.82/5 Rating |
|
Dec 22, 2024 Last updated |
Video Description: Equivalence relation for Mathematics 2024 is part of Mathematics for IIT JAM, GATE, CSIR NET, UGC NET preparation.
The notes and questions for Equivalence relation have been prepared according to the Mathematics exam syllabus.
Information about Equivalence relation covers all important topics for Mathematics 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Equivalence relation.
Introduction of Equivalence relation in English is available as part of our Mathematics for IIT JAM, GATE, CSIR NET, UGC NET for Mathematics & Equivalence relation in
Hindi for Mathematics for IIT JAM, GATE, CSIR NET, UGC NET course. Download more important topics related with notes, lectures and mock test series for
Mathematics Exam by signing up for free.
Description
Video Lecture & Questions for Equivalence relation Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET - Mathematics full syllabus preparation | Free video for Mathematics exam to prepare for Mathematics for IIT JAM, GATE, CSIR NET, UGC NET.
Information about Equivalence relation
Here you can find the meaning of Equivalence relation defined & explained in the simplest way possible.
Besides explaining types of Equivalence relation theory, EduRev gives you an ample number of questions to practice Equivalence relation tests,
examples and also practice Mathematics tests.
|
556 videos|198 docs
|
|
Explore Courses for Mathematics exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
CSIR NET
,CSIR NET
,Viva Questions
,UGC NET
,Extra Questions
,ppt
,GATE
,mock tests for examination
,study material
,UGC NET
,Equivalence relation Video Lecture | Mathematics for IIT JAM
,Important questions
,Exam
,video lectures
,shortcuts and tricks
,Free
,Sample Paper
,Objective type Questions
,CSIR NET
,Equivalence relation Video Lecture | Mathematics for IIT JAM
,UGC NET
,Semester Notes
,past year papers
,Previous Year Questions with Solutions
,GATE
,Summary
,Equivalence relation Video Lecture | Mathematics for IIT JAM
,MCQs
,practice quizzes
,GATE
;
Study Equivalence relation on the App
Students of Mathematics can study Equivalence relation alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Equivalence relation,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Equivalence relation is prepared as per the latest Mathematics syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup