Mathematics Exam > Mathematics Questions > Which one is a group under multiplication mod...
Start Learning for Free
Which one is a group under multiplication modulo 11?
- a){1,8}
- b){9,1}
- c){10,1}
- d){1,3,5,7,8}
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Which one is a group under multiplication modulo 11?a){1,8}b){9,1}c){1...
By the definition of operation table of a group.
Most Upvoted Answer
Which one is a group under multiplication modulo 11?a){1,8}b){9,1}c){1...
By the definition of operation table of a group.
Free Test
FREE
| Start Free Test |
Community Answer
Which one is a group under multiplication modulo 11?a){1,8}b){9,1}c){1...
Explanation:
Group under Multiplication Modulo 11:
- In a group under multiplication modulo 11, the set of elements should be relatively prime to 11 (i.e., the greatest common divisor of the element and 11 should be 1) and the set should be closed under multiplication modulo 11.
Analysis of Options:
a) {1, 8}
- 1 is relatively prime to 11 (gcd(1, 11) = 1)
- 8 is not relatively prime to 11 (gcd(8, 11) = 1)
- Therefore, this set does not form a group under multiplication modulo 11.
b) {9, 1}
- 9 is relatively prime to 11 (gcd(9, 11) = 1)
- 1 is relatively prime to 11 (gcd(1, 11) = 1)
- Therefore, this set forms a group under multiplication modulo 11.
c) {10, 1}
- 10 is relatively prime to 11 (gcd(10, 11) = 1)
- 1 is relatively prime to 11 (gcd(1, 11) = 1)
- Therefore, this set forms a group under multiplication modulo 11.
d) {1, 3, 5, 7, 8}
- Some elements in this set are not relatively prime to 11 (e.g., 8: gcd(8, 11) = 1)
- Therefore, this set does not form a group under multiplication modulo 11.
Conclusion:
The group under multiplication modulo 11 is {10, 1} as both elements are relatively prime to 11 and the set is closed under multiplication modulo 11.
Group under Multiplication Modulo 11:
- In a group under multiplication modulo 11, the set of elements should be relatively prime to 11 (i.e., the greatest common divisor of the element and 11 should be 1) and the set should be closed under multiplication modulo 11.
Analysis of Options:
a) {1, 8}
- 1 is relatively prime to 11 (gcd(1, 11) = 1)
- 8 is not relatively prime to 11 (gcd(8, 11) = 1)
- Therefore, this set does not form a group under multiplication modulo 11.
b) {9, 1}
- 9 is relatively prime to 11 (gcd(9, 11) = 1)
- 1 is relatively prime to 11 (gcd(1, 11) = 1)
- Therefore, this set forms a group under multiplication modulo 11.
c) {10, 1}
- 10 is relatively prime to 11 (gcd(10, 11) = 1)
- 1 is relatively prime to 11 (gcd(1, 11) = 1)
- Therefore, this set forms a group under multiplication modulo 11.
d) {1, 3, 5, 7, 8}
- Some elements in this set are not relatively prime to 11 (e.g., 8: gcd(8, 11) = 1)
- Therefore, this set does not form a group under multiplication modulo 11.
Conclusion:
The group under multiplication modulo 11 is {10, 1} as both elements are relatively prime to 11 and the set is closed under multiplication modulo 11.
|
Explore Courses for Mathematics exam
|
|
Which one is a group under multiplication modulo 11?a){1,8}b){9,1}c){10,1}d){1,3,5,7,8}Correct answer is option 'C'. Can you explain this answer?
Question Description
Which one is a group under multiplication modulo 11?a){1,8}b){9,1}c){10,1}d){1,3,5,7,8}Correct answer is option 'C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Which one is a group under multiplication modulo 11?a){1,8}b){9,1}c){10,1}d){1,3,5,7,8}Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one is a group under multiplication modulo 11?a){1,8}b){9,1}c){10,1}d){1,3,5,7,8}Correct answer is option 'C'. Can you explain this answer?.
Which one is a group under multiplication modulo 11?a){1,8}b){9,1}c){10,1}d){1,3,5,7,8}Correct answer is option 'C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Which one is a group under multiplication modulo 11?a){1,8}b){9,1}c){10,1}d){1,3,5,7,8}Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one is a group under multiplication modulo 11?a){1,8}b){9,1}c){10,1}d){1,3,5,7,8}Correct answer is option 'C'. Can you explain this answer?.
Solutions for Which one is a group under multiplication modulo 11?a){1,8}b){9,1}c){10,1}d){1,3,5,7,8}Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of Which one is a group under multiplication modulo 11?a){1,8}b){9,1}c){10,1}d){1,3,5,7,8}Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Which one is a group under multiplication modulo 11?a){1,8}b){9,1}c){10,1}d){1,3,5,7,8}Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Which one is a group under multiplication modulo 11?a){1,8}b){9,1}c){10,1}d){1,3,5,7,8}Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Which one is a group under multiplication modulo 11?a){1,8}b){9,1}c){10,1}d){1,3,5,7,8}Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Which one is a group under multiplication modulo 11?a){1,8}b){9,1}c){10,1}d){1,3,5,7,8}Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Mathematics tests.
|
|
Explore Courses for Mathematics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup