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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 =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} %3!

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 =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} %3!

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 14E: In each of the following parts, a relation is defined on the set of all human beings. Determine...
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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}
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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