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I have the following question and I also have the answer, I just dont understand why and how this question is approached, please elaborate more "Let R = ∅ be the empty relation on a nonempty set A. Which of the properties reflexive, symmetric and transitive does R possess?"

I have the following question and I also have the answer, I just dont understand why and how this question is approached, please elaborate more "Let R = ∅ be the empty relation on a nonempty set A. Which of the properties reflexive, symmetric and transitive does R possess?"

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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I have the following question and I also have the answer, I just dont understand why and how this question is approached, please elaborate more "Let R = ∅ be the empty relation on a nonempty set A. Which of the properties reflexive, symmetric and
transitive does R possess?"

 

 

Let set A is nonempty set and consider relation R given by R = 0. Then we can conclude thatthe relation R is symmetric because {0,0} € R. The only element of R is so relation is transitive. Since A is a nonempty set then relation R is not reflexible.
Transcribed Image Text:Let set A is nonempty set and consider relation R given by R = 0. Then we can conclude thatthe relation R is symmetric because {0,0} € R. The only element of R is so relation is transitive. Since A is a nonempty set then relation R is not reflexible.
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