For the function f : Z18 → Ze defined as f(r) = 4x+1 mod 6. Consider the relation R on the set Z18 defined as rRy when f(x) = f(y). Show that this relation is: (a) reflexive; (b) symmetric; (c) transitive; this will prove that R is an equivalence relation; finally (d) calculate its equivalence classes.
For the function f : Z18 → Ze defined as f(r) = 4x+1 mod 6. Consider the relation R on the set Z18 defined as rRy when f(x) = f(y). Show that this relation is: (a) reflexive; (b) symmetric; (c) transitive; this will prove that R is an equivalence relation; finally (d) calculate its equivalence classes.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 6TFE: Label each of the following statements as either true or false. Let R be a relation on a nonempty...
Related questions
Question
![5.
For the function f: Z18 → Ze defined as f(r) = 4x +1 mod 6. Consider the relation R on the set Z1s
defined as Ry when f(r) f(y). Show that this relation is:
(a) reflexive;
(b) symmetric;
(c) transitive;
this will prove that R is an equivalence relation; finally
(d) calculate its equivalence classes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c51e4a0-890f-4d8a-b0f1-054d53aa3d35%2F4eb387fc-60a9-4988-81de-bc1bacdfde26%2Fzq9dcqy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5.
For the function f: Z18 → Ze defined as f(r) = 4x +1 mod 6. Consider the relation R on the set Z1s
defined as Ry when f(r) f(y). Show that this relation is:
(a) reflexive;
(b) symmetric;
(c) transitive;
this will prove that R is an equivalence relation; finally
(d) calculate its equivalence classes.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Elements Of Modern Algebra](https://www.bartleby.com/isbn_cover_images/9781285463230/9781285463230_smallCoverImage.gif)
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
![Big Ideas Math A Bridge To Success Algebra 1: Stu…](https://www.bartleby.com/isbn_cover_images/9781680331141/9781680331141_smallCoverImage.jpg)
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
![Algebra for College Students](https://www.bartleby.com/isbn_cover_images/9781285195780/9781285195780_smallCoverImage.gif)
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
![Elements Of Modern Algebra](https://www.bartleby.com/isbn_cover_images/9781285463230/9781285463230_smallCoverImage.gif)
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
![Big Ideas Math A Bridge To Success Algebra 1: Stu…](https://www.bartleby.com/isbn_cover_images/9781680331141/9781680331141_smallCoverImage.jpg)
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
![Algebra for College Students](https://www.bartleby.com/isbn_cover_images/9781285195780/9781285195780_smallCoverImage.gif)
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning