Exercise 4.5. Let R be a irreflexive and transitive relation on the set S. Then R is a strict linear order on S if and only if for any two elements r and y exactly one of the following is true, (r, y) e R, (y, æ) e R, or x = y. This is the so-called trichotomy property,

Exercise 4.5. Let R be a irreflexive and transitive relation on the set S. Then R is a strict linear order on S if and only if for any two elements r and y exactly one of the following is true, (r, y) e R, (y, æ) e R, or x = y. This is the so-called trichotomy property,

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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Exercise 4.5. Let R be a irreflexive and transitive relation on the set S.
Then R is a strict linear order on S if and only if for any two elements r
and y exactly one of the following is true, (r, y) e R, (y, æ) e R, or x = y.
This is the so-called trichotomy property,

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