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 anequivalence relation iff it is circular and reflexive.

The relation on a set is a subset of the Cartesian product of the set. Therefore, each element is in…

Answered: A relation on a set A is circular iff ,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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.