I need answer of : d. Justifying your answer, find the smallest set of related pairs which must beadded to R in order for it to become an equivalence relation. Question 7Let R be the relation on the set S = {1,2,3, a, b, c} given byx Ry if and only if(г, у) € {(а, а), (1,1), (а, 1), (1, а), (3, 1), (1,3), (3, а), (а, 3), (ь, b), (ь, 2), (2, с)}6.(a) Draw a digraph representing the relation R.(b) Show that R is not transitive.(c) Justifying your answer, find the smallest set of related pairs which must beadded to Rin order for it to become transitive.(d) Justifying your answer, find the smallest set of related pairs which must beadded to R in order for it to become an equivalence relation.

We know that a relation is called an equivalence relation if it is reflexive, symmetric and…

Answered: (d) Justifying your answer, find the…

(d) Justifying your answer, find the smallest set of related pairs which must be added to R in order for it to become an equivalence relation.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 14E: In each of the following parts, a relation is defined on the set of all human beings. Determine...

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Question

I need answer of :

d. Justifying your answer, find the smallest set of related pairs which must be
added to R in order for it to become an equivalence relation.

Question 7
Let R be the relation on the set S = {1,2,3, a, b, c} given by
x Ry if and only if
(г, у) € {(а, а), (1,1), (а, 1), (1, а), (3, 1), (1,3), (3, а), (а, 3), (ь, b), (ь, 2), (2, с)}
6.
(a) Draw a digraph representing the relation R.
(b) Show that R is not transitive.
(c) Justifying your answer, find the smallest set of related pairs which must be
added to Rin order for it to become transitive.
(d) Justifying your answer, find the smallest set of related pairs which must be
added to R in order for it to become an equivalence relation.

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