(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.

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter8: Introduction To Functions
Section8.8: Linear And Quadratic Functions
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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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