4.relation.Show that if a relation p on a set S is reflexive and circular, then it is an equivalence2

To show that if a relation ρ on a set S is reflexive and circular, then it is an equivalence…

Answered: 4. relation. Show that if a relation p…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...

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Similar questions

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.
Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.
In each of the following parts, a relation is defined on the set of all human beings. Determine whether the relation is reflective, symmetric, or transitive. Justify your answers. xRy if and only if x lives within 400 miles of y. xRy if and only if x is the father of y. xRy if and only if x is a first cousin of y. xRy if and only if x and y were born in the same year. xRy if and only if x and y have the same mother. xRy if and only if x and y have the same hair colour.
Determine whether the set S={1,x2,2+x2} spans P2.
Let A=R0, the set of all nonzero real numbers, and consider the following relations on AA. Decide in each case whether R is an equivalence relation, and justify your answers. (a,b)R(c,d) if and only if ad=bc. (a,b)R(c,d) if and only if ab=cd. (a,b)R(c,d) if and only if a2+b2=c2+d2. (a,b)R(c,d) if and only if ab=cd.
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?
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 , prove the statements concerning the relation on the set of all integers. 17. If and , then .
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.
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.
In Exercises 1324, prove the statements concerning the relation on the set Z of all integers. If 0xy, then x2y2.
True or False Label each of the following statements as either true or false. 2. Every relation on a nonempty set is as mapping.

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4. relation. Show that if a relation p on a set S is reflexive and circular, then it is an equivalence 2