If R is a symmetric relation, which statement about R ∪ R⁻¹ is correct?
Answer and explanation
Correct answer: It is equal to R
For any relation, R⁻¹ is obtained by reversing ordered pairs. Since R is symmetric, reversing its pairs produces no new pairs and gives R⁻¹ = R. Substituting this into the expression yields R ∪ R⁻¹ = R ∪ R. The union of a set with itself is the set itself, so the expression equals R. It is not necessarily empty or universal.
Frequently asked questions
What is the correct answer to this question?
It is equal to R
Why is this the correct answer?
For any relation, R⁻¹ is obtained by reversing ordered pairs. Since R is symmetric, reversing its pairs produces no new pairs and gives R⁻¹ = R. Substituting this into the expression yields R ∪ R⁻¹ = R ∪ R. The union of a set with itself is the set itself, so the expression equals R. It is not necessarily empty or universal.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Symmetric relation.
