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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.

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.

Advanced Engineering Mathematics
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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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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