Answer it all. Determine whether the relation R on the set of all integers is reflexive, symmetric,antisymmetric and transitive where (x, y) e R if and only if(a) x + y2.(b)X = y + 2 or x = y - 2(c)x is divisible by y.

Answered: Image /qna-images/answer/a170309f-e01a-4367-b162-3cbdc97a60f3.jpg

Answered: Determine whether the relation R on the…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 20E: Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not...

See similar textbooks

Similar questions

For any relation on the nonempty set, the inverse of is the relation defined by if and only if . Prove the following statements. is symmetric if and only if . is antisymmetric if and only if is a subset of . is asymmetric if and only if .
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.
21. A relation on a nonempty set is called irreflexive if for all. Which of the relations in Exercise 2 are irreflexive? 2. In each of the following parts, a relation is defined on the set of all integers. Determine in each case whether or not is reflexive, symmetric, or transitive. Justify your answers. a. if and only if b. if and only if c. if and only if for some in . d. if and only if e. if and only if f. if and only if g. if and only if h. if and only if i. if and only if j. if and only if. k. if and only if.
Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.
In Exercises , prove the statements concerning the relation on the set of all integers. 18. If and , then .
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.
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.
2. In each of the following parts, a relation is defined on the set of all integers. Determine in each case whether or not is reflexive, symmetric or transitive. Justify your answers. a. if and only if . b. if and only if . c. if and only if for some in . d. if and only if . e. if and only if . f. if and only if . g. if and only if . h. if and only if . i. if and only if . j. if and only if . k. if and only if .

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

Determine whether the relation R on the set of all integers is reflexive, symmetric, antisymmetric and transitive where (x, y) e R if and only if (a) x + y 2. (b) X = y + 2 or x = y - 2 (c) x is divisible by y.