Determine whether the relation is reflexive, symmetric, antisymmetric and transitive. Provide one counterexample for each property that the relation is not. 1. Relation R on the set {1, 2, 3, 4}, where R {(1,3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)} ........ 2. Relation R on the set {1, 2, 3, 4}, where R = {(1, 3), (3, 1)} 3. Relation R on the set of integers, where aRy iff æ = 2y ......
Determine whether the relation is reflexive, symmetric, antisymmetric and transitive. Provide one counterexample for each property that the relation is not. 1. Relation R on the set {1, 2, 3, 4}, where R {(1,3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)} ........ 2. Relation R on the set {1, 2, 3, 4}, where R = {(1, 3), (3, 1)} 3. Relation R on the set of integers, where aRy iff æ = 2y ......
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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Transcribed Image Text:Determine whether the relation is reflexive, symmetric, antisymmetric and transitive. Provide one counterexample for
each property that the relation is not.
1. Relation R on the set {1, 2, 3, 4}, where R = {(1,3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)}
2. Relation R on the set {1, 2, 3, 4}, where R = {(1, 3), (3, 1)}
3. Relation R on the set of integers, where aRy iff æ = 2y
......
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