Mathematics Exam > Mathematics Videos > Mathematics for Competitive Exams > Elementary Properties of Groups
Elementary Properties of Groups Video Lecture | Mathematics for Competitive Exams
|
98 videos|27 docs|30 tests
|
FAQs on Elementary Properties of Groups Video Lecture - Mathematics for Competitive Exams
| 1. What are the four elementary properties of groups? |  |
Ans. The four elementary properties of groups are closure, associativity, identity element, and inverse element. Closure means that the operation between any two elements of the group will always result in another element within the group. Associativity means that the order in which the operations are performed does not affect the final result. Identity element is an element in the group that, when combined with any other element, leaves the other element unchanged. Inverse element is an element in the group that, when combined with another element, results in the identity element.
| 2. How does closure property ensure that a group is closed under the operation? | |
Ans. The closure property ensures that a group is closed under the operation by guaranteeing that the result of the operation between any two elements of the group will always be another element within the group. This means that for any two elements, a and b, in the group, their operation, denoted as a * b, will also be an element of the group. If the group is not closed under the operation, it cannot be considered a group.
| 3. What is the significance of the identity element in a group? | |
Ans. The identity element in a group is significant because it serves as a neutral element for the group's operation. When any element of the group is combined with the identity element, it remains unchanged. In other words, the identity element acts as a "do-nothing" element. It ensures that every element in the group has an element it can combine with to produce itself. The identity element is unique within the group and is an essential property of a group.
| 4. How does the inverse element relate to the identity element in a group? | |
Ans. The inverse element in a group is closely related to the identity element. For every element a in a group, there exists an element b, called the inverse of a, such that the operation between a and b results in the identity element of the group. In other words, a * b = b * a = identity element. The inverse element "undoes" the operation with a particular element and brings it back to the neutral state represented by the identity element.
| 5. Can you provide an example of a group that satisfies all the elementary properties? | |
Ans. Yes, one example of a group that satisfies all the elementary properties is the set of integers under addition, denoted as (Z, +). The closure property holds because the sum of any two integers is always an integer. Associativity holds because the order of addition does not affect the result. The identity element is 0, as adding 0 to any integer leaves the integer unchanged. Finally, every integer has an inverse element, where the inverse of an integer x is -x, as x + (-x) = 0.
Related Exams
About this Video
|
4.98/5 Rating |
|
Dec 23, 2024 Last updated |
Video Description: Elementary Properties of Groups for Mathematics 2024 is part of Mathematics for Competitive Exams preparation.
The notes and questions for Elementary Properties of Groups have been prepared according to the Mathematics exam syllabus.
Information about Elementary Properties of Groups covers all important topics for Mathematics 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Elementary Properties of Groups.
Introduction of Elementary Properties of Groups in English is available as part of our Mathematics for Competitive Exams for Mathematics & Elementary Properties of Groups in
Hindi for Mathematics for Competitive Exams 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 Elementary Properties of Groups Video Lecture | Mathematics for Competitive Exams - Mathematics full syllabus preparation | Free video for Mathematics exam to prepare for Mathematics for Competitive Exams.
Information about Elementary Properties of Groups
Here you can find the meaning of Elementary Properties of Groups defined & explained in the simplest way possible.
Besides explaining types of Elementary Properties of Groups theory, EduRev gives you an ample number of questions to practice Elementary Properties of Groups tests,
examples and also practice Mathematics tests.
|
98 videos|27 docs|30 tests
|
|
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
Summary
,study material
,Viva Questions
,ppt
,Elementary Properties of Groups Video Lecture | Mathematics for Competitive Exams
,past year papers
,Elementary Properties of Groups Video Lecture | Mathematics for Competitive Exams
,Previous Year Questions with Solutions
,video lectures
,Semester Notes
,Exam
,Elementary Properties of Groups Video Lecture | Mathematics for Competitive Exams
,Extra Questions
,MCQs
,mock tests for examination
,Free
,practice quizzes
,shortcuts and tricks
,Important questions
,Objective type Questions
,Sample Paper
;
Study Elementary Properties of Groups on the App
Students of Mathematics can study Elementary Properties of Groups alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Elementary Properties of Groups,
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 Elementary Properties of Groups 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