1. Consider the relation R on the set A = {0,1, 2, 3, 4}, defined by: %3D aRb + a = bc and b= ad, for some c, d e A. (a) Is R an equivalence relation on A? If so, prove it. If not, show why not. (b) Is R a partial ordering on A? If so, prove it and draw the Hasse diagram. If not, show why not.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 10E: In Exercises , a relation is defined on the set of all integers. In each case, prove that is an...
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1. Consider the relation R on the set A = {0,1, 2, 3, 4}, defined by:
aRb + a = bc and b= ad, for some c, d e A.
(a) Is R an equivalence relation on A? If so, prove it. If not, show why not.
(b) Is R a partial ordering on A? If so, prove it and draw the Hasse diagram. If not,
show why not.
Transcribed Image Text:1. Consider the relation R on the set A = {0,1, 2, 3, 4}, defined by: aRb + a = bc and b= ad, for some c, d e A. (a) Is R an equivalence relation on A? If so, prove it. If not, show why not. (b) Is R a partial ordering on A? If so, prove it and draw the Hasse diagram. If not, show why not.
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