Define a relation R on Z as follows: For all integers mandmRn2n.а.п,т —Then 6R3ΟΑ. ΤηueO B. FalseDefine R as above.Then 5R10A. TrueB. FalseDefine R as above. R is not symmetric.A. TrueB. False

Given mRn ⇔ m = 2n where m, n are integers and R is the relation.

Answered: Define a relation R on Z as follows:…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 24E: For any relation on the nonempty set, the inverse of is the relation defined by if and only if ....

See similar textbooks

Similar questions

A relation R on a nonempty set A is called asymmetric if, for x and y in A, xRy implies yRx. Which of the relations in Exercise 2 areasymmetric? In each of the following parts, a relation R is defined on the set of all integers. Determine in each case whether or not R is reflexive, symmetric, or transitive. Justify your answers. a. xRy if and only if x=2y. b. xRy if and only if x=y. c. xRy if and only if y=xk for some k in . d. xRy if and only if xy. e. xRy if and only if xy. f. xRy if and only if x=|y|. g. xRy if and only if |x||y+1|. h. xRy if and only if xy i. xRy if and only if xy j. xRy if and only if |xy|=1. k. xRy if and only if |xy|1.
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.
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 .
For each of the following relations R defined on the set A of all triangles in a plane, determine whether R is reflexive, symmetric, or transitive. Justify your answers. a. aRb if and only if a is similar to b. b. aRb if and only if a is congruent to b.
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

Define a relation R on Z as follows: For all integers m and n, mRn m= n = 2n. а. Then 6R3 Α. True O B. False Define R as above. Then 5R10 A. True O B. False Define R as above. R is not symmetric. A. True B. False