I have the following questions: " Let R = ∅ be the empty relation on a nonempty set A. Which of the properties reflexive, symmetric and transitive does R possess?" and the following answer is given: "Let set A is nonempty set and consider relation R given by R=∅. Then we can conclude that the relation R is symmetric because {∅,∅}∈R. The only element of R is ∅ so relation is transitive. Since A is a nonempty set then relation R is not reflexible." How can it be any propert when the set is empty? don't you need pairs to decide which property the set holds?

I have the following questions: " Let R = ∅ be the empty relation on a nonempty set A. Which of the properties reflexive, symmetric and transitive does R possess?" and the following answer is given: "Let set A is nonempty set and consider relation R given by R=∅. Then we can conclude that the relation R is symmetric because {∅,∅}∈R. The only element of R is ∅ so relation is transitive. Since A is a nonempty set then relation R is not reflexible." How can it be any propert when the set is empty? don't you need pairs to decide which property the set holds?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 14E: In each of the following parts, a relation is defined on the set of all human beings. Determine...

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