Let A be nonempty and let R be the empty relation on A. Which statement is correct?
Answer and explanation
Correct answer: R is symmetric and irreflexive
The empty relation is symmetric vacuously: there is no pair (a,b) in R that could violate the requirement that (b,a) also be present. Since A is nonempty, at least one diagonal pair (a,a) is required for reflexivity, but none is in R, so R is irreflexive. Therefore option A is correct; it is not reflexive or an equivalence relation.
Frequently asked questions
What is the correct answer to this question?
R is symmetric and irreflexive
Why is this the correct answer?
The empty relation is symmetric vacuously: there is no pair (a,b) in R that could violate the requirement that (b,a) also be present. Since A is nonempty, at least one diagonal pair (a,a) is required for reflexivity, but none is in R, so R is irreflexive. Therefore option A is correct; it is not reflexive or an equivalence relation.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Types of relations.
