In the following questions, determine whether the binary relation is: (1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive. Justify your answer. 1. Let S be the set of all integers. Let relation R on the set S be: R= {(x,y)|x+y>10}. 2. Let S be the set of all integers. Let relation R on the set S be: R = {(x,y) | y divides x} 3. Let S be the set of all integers. Let relation R on the set S be: R = {(x,y) | x² =y²} %3! %3D
In the following questions, determine whether the binary relation is: (1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive. Justify your answer. 1. Let S be the set of all integers. Let relation R on the set S be: R= {(x,y)|x+y>10}. 2. Let S be the set of all integers. Let relation R on the set S be: R = {(x,y) | y divides x} 3. Let S be the set of all integers. Let relation R on the set S be: R = {(x,y) | x² =y²} %3! %3D
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:In the following questions, determine whether the binary relation is: (1) reflexive, (2)
symmetric, (3) antisymmetric, (4) transitive. Justify your answer.
1. Let S be the set of all integers. Let relation R on the set S be: R ={(x,y)|x+y>10}.
2. Let S be the set of all integers. Let relation R on the set S be: R = {(x,y) | y divides x}
3. Let S be the set of all integers. Let relation R on the set S be: R = {(x,y) | x? =y?}
4. Let S denote the set of all people in Canada. Let relation R on the set S be: R={(x,y)|x has
the same father as y}
5. Let S be the set of all Sheridan classes. Let relation R on the set S be: R = {(x,y)| the
number of students in classes x and y do not differ by more than one}
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