A relation on a set A is circular iff , y, z x~y and y~z implies z~x. Prove that a relation is an equivalence relation iff it is circular and reflexive.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...
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A relation on a set A is circular iff Vx, y, z x~y and y~z implies z-x. Prove that a relation is an
equivalence relation iff it is circular and reflexive.
Transcribed Image Text:A relation on a set A is circular iff Vx, y, z x~y and y~z implies z-x. Prove that a relation is an equivalence relation iff it is circular and reflexive.
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