please solve Let A = {0,1, 2} × {0, 1, 2, 3}. We define an equivalence relation R on A by saying that(a, b)R(c, d) if and only if 2a – b = 2c – d. No need to show that this is an equivalencerelation. Write down the equivalence classes for R.

Answered: Image /qna-images/answer/a08f9dc8-6f30-4bfe-8893-8c5efeecbbcd.jpg

Answered: Let A = {0,1, 2} × {0, 1, 2, 3}. We…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.3: Subgroups

Problem 23E: 23. Let be the equivalence relation on defined by if and only if there exists an element in ...

See similar textbooks

Similar questions

23. Let be the equivalence relation on defined by if and only if there exists an element in such that .If , find , the equivalence class containing.
Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide whether or not is an equivalence relation. Justify your decision.
Label each of the following statements as either true or false. Let R be a relation on a nonempty set A that is symmetric and transitive. Since R is symmetric xRy implies yRx. Since R is transitive xRy and yRx implies xRx. Hence R is alsoreflexive and thus an equivalence relation on A.
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.
Prove Theorem 1.40: If is an equivalence relation on the nonempty set , then the distinct equivalence classes of form a partition of .
True or False Label each of the following statements as either true or false. Let be an equivalence relation on a nonempty setand let and be in. If, then.
In Exercises 610, a relation R is defined on the set Z of all integers, In each case, prove that R is an equivalence relation. Find the distinct equivalence classes of R and least four members of each. xRy if and only if x2+y2 is a multiple of 2.
In Exercises , a relation is defined on the set of all integers. In each case, prove that is an equivalence relation. Find the distinct equivalence classes of and list at least four members of each. 10. if and only if .
Label each of the following statements as either true or false. If R is an equivalence relation on a nonempty set A, then any two equivalence classes of R contain the same number of element.
True or False Label each of the following statements as either true or false. If is an equivalence relation on a nonempty set, then the distinct equivalence classes of form a partition of.

Recommended textbooks for you

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

SEE MORE TEXTBOOKS

Let A = {0,1, 2} × {0, 1, 2, 3}. We define an equivalence relation R on A by saying that (a, b)R(c, d) if and only if 2a – b = 2c – d. No need to show that this is an equivalence relation. Write down the equivalence classes for R.