Which is the definition of a transitive relation? 2 x~y⇒y~x for all x, y E X. x~y and y~ x⇒x~z for all x, y, z € X. x~y and y~z⇒x~z for all x, y, z € X. xy and y~ x⇒y~z for all x, y, z € X. None of the above
Which is the definition of a transitive relation? 2 x~y⇒y~x for all x, y E X. x~y and y~ x⇒x~z for all x, y, z € X. x~y and y~z⇒x~z for all x, y, z € X. xy and y~ x⇒y~z for all x, y, z € X. None of the above
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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![Which is the definition of a transitive relation?
O
O
x ~ y⇒ y ~ x for all x, y € X.
x~y and y~ x⇒ x~z for all x, y, z € X.
x~y and y~ z⇒ x ~ z for all x, y, z € X.
x ~y and y~ x ⇒ y ~ z for all x, y, z € X.
None of the above](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea7bbfe4-f0d9-4343-839c-f9e5c129de8e%2F2b37ab82-2f50-4af1-a15d-8799df22ecb5%2Fulwnbt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Which is the definition of a transitive relation?
O
O
x ~ y⇒ y ~ x for all x, y € X.
x~y and y~ x⇒ x~z for all x, y, z € X.
x~y and y~ z⇒ x ~ z for all x, y, z € X.
x ~y and y~ x ⇒ y ~ z for all x, y, z € X.
None of the above
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