Please Help ASAP!!! A binary relation < on a set X is said to be a preorder if it is reflexive and transitive.For example, let X denote the collection of all living earthlings and let < be defined asfollows: V x, y € X, x < y if and only if x is no older than y, where age is measured inwhole days. Clearly < is reflexive and transitive, but it is not symmetric (since youngerdoesn't imply older) nor antisymmetric (since different people may be the same age).But prove the following.Theorem. Let < be a preorder on a set X. Define the relation =, where x = y holds ifand only if x

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Answered: Theorem. Let < be a preorder on a set…

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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Theorem. Let < be a preorder on a set X. Define the relation =, where x = y holds if and only if x < y and y < x. Then = is an equivalence relation on X.