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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,

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
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,
Transcribed Image Text: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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