(a) Give an example of a relation on the set {a,b, c, d} which is symmetric andtransitive, but not reflexive.(b) Let R be the equivalence relation on the set S = {1,3,5, 7, ... , 49} defined byx Ry if and only if x = y (mod 10).Give the equivalence classes for the relation R on S.Justify your answers!

a) Definition of symmetric, transitive, reflexive relation: Let, R be a relation on A. R is said to…

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{a,b, c, d} which is symmetric and (a) Give an transitive, but not reflexive. example of a relation on the set

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

(a) Give an example of a relation on the set {a,b, c, d} which is symmetric and
transitive, but not reflexive.
(b) Let R be the equivalence relation on the set S = {1,3,5, 7, ... , 49} defined by
x Ry if and only if x = y (mod 10).
Give the equivalence classes for the relation R on S.
Justify your answers!

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