(a) Consider the relation R on the set A = {p, q, r, s} defined by R= {(p, p), (p, q), (q, r), (r, s), (r, T), (s, t)}. This relation is not reflexive. What element(s) would we need to add to R in order for it to be reflexive? (b) Consider the relation R on the set A = {X, Y, Z} defined by R = {(X, X), (X,Y), (X, Z), (Y,Y), (Y,Z), (Z, X)}. This relation is not symmetric. What element(s) would we need to add to R in order for it to be symmetric? (c) Consider the relation R on the set A = {X, Y, Z} defined by R = {(X,Y), (Y, X), (Z, Z)}. This relation is not transitive. What element(s) would we need to add to R in order for it to be transitive?

(a) Consider the relation R on the set A = {p, q, r, s} defined by R= {(p, p), (p, q), (q, r), (r, s), (r, T), (s, t)}. This relation is not reflexive. What element(s) would we need to add to R in order for it to be reflexive? (b) Consider the relation R on the set A = {X, Y, Z} defined by R = {(X, X), (X,Y), (X, Z), (Y,Y), (Y,Z), (Z, X)}. This relation is not symmetric. What element(s) would we need to add to R in order for it to be symmetric? (c) Consider the relation R on the set A = {X, Y, Z} defined by R = {(X,Y), (Y, X), (Z, Z)}. This relation is not transitive. What element(s) would we need to add to R in order for it to be transitive?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 13E: 13. Consider the set of all nonempty subsets of . Determine whether the given relation on is...

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