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(Relations) Consider the set A = {1,2, 3, 4, 5}, and a relation R defined by x Ry + x² – y is an integer multiple of 3. (a) List all elements y for which 1Ry is true. (b) Is R reflexive? Justify. (c) Is R symmetric? Justify.

(Relations) Consider the set A = {1,2, 3, 4, 5}, and a relation R defined by x Ry + x² – y is an integer multiple of 3. (a) List all elements y for which 1Ry is true. (b) Is R reflexive? Justify. (c) Is R symmetric? Justify.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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7. (Relations) Consider the set A= {1,2, 3, 4, 5}, and a relation R defined by x Ry x2 – y is an integer multiple of 3. (a) List all elements y for which 1Ry is true. (b) Is R reflexive? Justify. (c) Is R symmetric? Justify. (d) Is R antisymmetric? Justify. (e) Is R transitive? Justify.
Transcribed Image Text:7. (Relations) Consider the set A= {1,2, 3, 4, 5}, and a relation R defined by x Ry x2 – y is an integer multiple of 3. (a) List all elements y for which 1Ry is true. (b) Is R reflexive? Justify. (c) Is R symmetric? Justify. (d) Is R antisymmetric? Justify. (e) Is R transitive? Justify.
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