For any relation R, which statement about R ∪ R⁻¹ is always true?
Answer and explanation
Correct answer: It is symmetric
The governing concept is symmetry: a relation S is symmetric when (a,b) ∈ S implies (b,a) ∈ S. If (a,b) belongs to R, then (b,a) belongs to R⁻¹; if (a,b) belongs to R⁻¹, then (b,a) belongs to R. Thus every pair in R ∪ R⁻¹ brings its reverse pair into the same union. Therefore option A is always true. Reflexivity and transitivity are not guaranteed, and the union need not be empty.
Frequently asked questions
What is the correct answer to this question?
It is symmetric
Why is this the correct answer?
The governing concept is symmetry: a relation S is symmetric when (a,b) ∈ S implies (b,a) ∈ S. If (a,b) belongs to R, then (b,a) belongs to R⁻¹; if (a,b) belongs to R⁻¹, then (b,a) belongs to R. Thus every pair in R ∪ R⁻¹ brings its reverse pair into the same union. Therefore option A is always true. Reflexivity and transitivity are not guaranteed, and the union need not be empty.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Symmetric relation.
