6. Consider the set A = 10 = {0, 1, 2, ..., 9} and consider the relation R on A determined by a Rb if and only if a - b is a multiple of 3. (a) Represent the relation R as a subset of A × A (draw the corresponding table). (b) Show that R is reflexive, that is, for all a € A, we have a Ra. (c) Show that R is symmetric, that is, for all a, b = A, we have that a R b implies that b R a.

6. Consider the set A = 10 = {0, 1, 2, ..., 9} and consider the relation R on A determined by a Rb if and only if a - b is a multiple of 3. (a) Represent the relation R as a subset of A × A (draw the corresponding table). (b) Show that R is reflexive, that is, for all a € A, we have a Ra. (c) Show that R is symmetric, that is, for all a, b = A, we have that a R b implies that b R a.

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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