For each of the following relations, determine if they are reflexive, symmetric, antisymmetric, and/or transitive. Also indicate if the relation is an equivalence relation or not.
For each of the following relations, determine if they are reflexive, symmetric, antisymmetric, and/or transitive. Also indicate if the relation is an equivalence relation or not.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
For each of the following relations, determine if they are reflexive,
symmetric, antisymmetric, and/or transitive. Also indicate if the relation is an equivalence relation
or not.
symmetric, antisymmetric, and/or transitive. Also indicate if the relation is an equivalence relation
or not.
![a. {(x, y) | x=Ly]}
on the set of real numbers
b. {(m, n) | m² = n² }
on the set of integers
c. {(a, b) | classroom a has a larger capacity than classroom b}
d. {(1, 1), (2, 2), (1, 2), (2, 3), (3, 2), (3, 3)}
on the set of classrooms
on the set {1, 2, 3}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F416064f9-c57b-46ee-9b50-14b257515654%2Fafc4493a-e218-4ded-876c-42390019c544%2Fadz0f9q_processed.png&w=3840&q=75)
Transcribed Image Text:a. {(x, y) | x=Ly]}
on the set of real numbers
b. {(m, n) | m² = n² }
on the set of integers
c. {(a, b) | classroom a has a larger capacity than classroom b}
d. {(1, 1), (2, 2), (1, 2), (2, 3), (3, 2), (3, 3)}
on the set of classrooms
on the set {1, 2, 3}
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