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
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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please send handwritten solution for part c
![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}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca647657-5dac-449a-afc5-6e7781ff8242%2F7a2a6c40-3edd-4514-a6ac-3f9c0e676482%2Froosxl_processed.jpeg&w=3840&q=75)
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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