Determine whether the given relation isan equivalent relation on (1, 2, 3, 4, 5}If the relation is an equivalencerelation, list the equivalence classes(x, y E {1,2, 3, 4, 5} . )3, 4, 5}.1. {(1,1), (2, 2) , (3, 3) , (4, 4) , (5, 5) , (1, 3) , (3, 1)}2. {(x, y) | 3 divides x + y}

To find: (i)the given relation is equivalence or not. (ii) The equivalence class.

Answered: Determine whether the given relation is…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 27E: Prove Theorem 1.40: If is an equivalence relation on the nonempty set , then the distinct...

See similar textbooks

Similar questions

Does the relation is a brother of have a reflexive property consider one male? A symmetric property consider two males? A transitive property consider three males?
a. Let R be the equivalence relation defined on Z in Example 2, and write out the elements of the equivalence class [ 3 ]. b. Let R be the equivalence relation congruence modulo 4 that is defined on Z in Example 4. For this R, list five members of equivalence class [ 7 ].
Does the relation is in love with have a reflexive property consider one person? a symmetric property consider two people? a transitive property consider three people?
Prove Theorem 1.40: If is an equivalence relation on the nonempty set , then the distinct equivalence classes of form a partition of .
Let and be lines in a plane. Decide in each case whether or not is an equivalence relation, and justify your decisions. if and only ifand are parallel. if and only ifand are perpendicular.
Which of these relations on the set {0, 1, 2, 3} are equivalence relations? Determine the properties of an equivalence relation that the others lack. a) {(0, 0), (1, 1), (1, 2), (2, 1), (2, 2), (3, 3)} b) {(0, 0), (1, 1), (1, 3), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)} c) {(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0),(2, 2), (3, 3)}
Which of these relations on {0,1,2,3} are equivalence relations or a partial order? Determine the properties of an equivalence relation or partial order that the others lack a.{(0,0),(1,1),(2,2),(3,3)} b. {(0,0),(0,2),(2,0),(2,2),(2,3),(3,2),(3,3)} c. {(0,0),(1,1),(1,2),(2,1),(2,2),(3,3)} d. {(0,0),(1,1),(1,3),(2,2),(2,3),(3,1),(3,2),(3,3)} e. {(0,0),(0,1),(0,2),(1,0),(1,1),(1,2),(2,0),(2,2),(3,3)}
Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show which qualities of an equivalence relation it lacks: a. {(0, 0), (1, 1), (1, 2), (2, 1), (2, 2), (3, 3)} b. { (0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 2), (3, 3)}
Find the smallest relation containing the relation {(1, 2), (2, 3), (2, 4), (3, 1)} on theset {1, 2, 3, 4} that is reflexive, symmetric and transitive.
Let A = {0,1,2,3} and R a relation over A: R = {(0,0),(0,1),(0,3),(1,1),(1,0),(2,3),(3,3)} Check whether R is an equivalence relation or a partial order. Give a counterexample in each case in which the relation does not satisfy one of the properties of being an equivalence relation or a partial order.
b) If X = \{a,b,c\}X={a,b,c}, give the equivalence classes of the relation.
The relation R defined on Z by aRb if 3 | (2a + 7b) is an equivalence relation. the equivalence classes are: {0,±3,±6,…},{1,−2,4,−5,7,−8,10,…},{2,−1,5,−4,8,−7,11,…} How do they get these numbers and where do you begin?

SEE MORE QUESTIONS

Recommended textbooks for you

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

Elementary Geometry For College Students, 7e

Geometry

ISBN:

9781337614085

Author:

Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:

Cengage,

Elementary Geometry for College Students

Geometry

ISBN:

9781285195698

Author:

Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:

Cengage Learning

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

Elementary Geometry For College Students, 7e

Geometry

ISBN:

9781337614085

Author:

Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:

Cengage,

Elementary Geometry for College Students

Geometry

ISBN:

9781285195698

Author:

Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

Determine whether the given relation is an equivalent relation on {1, 2, 3, 4, 5} If the relation is an equivalence relation, list the equivalence classes (x, y = {1, 2, 3, 4, 5}.)