8. Let A = {1, 2, 3, 4, 5}. (a) Determine, with justification, if the following relation is reflexive. R= = {(1, 1), (1, 2), (3, 1), (2, 2), (5, 4), (4,4), (5,5), (3, 2), (3, 4), (2,5), (2, 1)} (b) Determine, with justification, if the following relation is symmetric. R = {(1, 1), (2, 2), (2, 3), (3, 2), (4, 5), (5, 1), (3, 4), (5, 4), (1, 5), (4,4)} (c) Determine, with justification, if the following relation is antisymmetric. R = {(2, 2), (3, 1), (1, 1), (3, 3), (5, 4), (5,5), (2, 4), (4, 3), (4,5)} (d) Determine, with justification, if the following relation is transitive. R = {(1,2), (2, 3), (1, 3), (4,4), (3, 4), (3, 5), (1, 4), (2,4)}
8. Let A = {1, 2, 3, 4, 5}. (a) Determine, with justification, if the following relation is reflexive. R= = {(1, 1), (1, 2), (3, 1), (2, 2), (5, 4), (4,4), (5,5), (3, 2), (3, 4), (2,5), (2, 1)} (b) Determine, with justification, if the following relation is symmetric. R = {(1, 1), (2, 2), (2, 3), (3, 2), (4, 5), (5, 1), (3, 4), (5, 4), (1, 5), (4,4)} (c) Determine, with justification, if the following relation is antisymmetric. R = {(2, 2), (3, 1), (1, 1), (3, 3), (5, 4), (5,5), (2, 4), (4, 3), (4,5)} (d) Determine, with justification, if the following relation is transitive. R = {(1,2), (2, 3), (1, 3), (4,4), (3, 4), (3, 5), (1, 4), (2,4)}
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter1: Line And Angle Relationships
Section1.6: Relationships: Perpendicular Lines
Problem 18E: Does the relation is in love with have a reflexive property consider one person? a symmetric...
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Transcribed Image Text:8. Let A = {1, 2, 3, 4, 5).
(a) Determine, with justification, if the following relation is reflexive.
R=
= {(1, 1), (1, 2), (3, 1), (2, 2), (5, 4), (4, 4), (5, 5), (3, 2), (3, 4), (2, 5), (2, 1)}
(b) Determine, with justification, if the following relation is symmetric.
R = {(1, 1), (2, 2), (2, 3), (3, 2), (4, 5), (5, 1), (3, 4), (5, 4), (1, 5), (4,4)}
(c) Determine, with justification, if the following relation is antisymmetric.
R = {(2, 2), (3, 1), (1, 1), (3, 3), (5, 4), (5, 5), (2, 4), (4, 3), (4,5)}
(d) Determine, with justification, if the following relation is transitive.
R = {(1, 2), (2, 3), (1, 3), (4, 4), (3, 4), (3, 5), (1, 4), (2,4)}
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