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Define a relation Ton the set of real numbers as follows: Vx, y ≤R, x Ty ⇒xy < 0 The relation is not transitive since we can provide a counter example. The relation T is transitive. We can write a formal proof The relation is not transitive. take x=1 and y=-1 then xy=yx The relation is transitive. If we take x=-1, y=1, xy=-1 which is smaller than 0.

Define a relation Ton the set of real numbers as follows: Vx, y ≤R, x Ty ⇒xy < 0 The relation is not transitive since we can provide a counter example. The relation T is transitive. We can write a formal proof The relation is not transitive. take x=1 and y=-1 then xy=yx The relation is transitive. If we take x=-1, y=1, xy=-1 which is smaller than 0.

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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Define a relation Ton the set of real numbers as follows: Vx, y ≤R, x Ty ⇒xy < 0 The relation is not transitive since we can provide a counter example. The relation T is transitive. We can write a formal proof The relation is not transitive. take x=1 and y=-1 then xy=yx The relation is transitive. If we take x=-1, y=1, xy=-1 which is smaller than 0.
Transcribed Image Text:Define a relation Ton the set of real numbers as follows: Vx, y ≤R, x Ty ⇒xy < 0 The relation is not transitive since we can provide a counter example. The relation T is transitive. We can write a formal proof The relation is not transitive. take x=1 and y=-1 then xy=yx The relation is transitive. If we take x=-1, y=1, xy=-1 which is smaller than 0.
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