For any relation R, which statement about R∪R⁻¹ is always true?
Answer and explanation
Correct answer: It is symmetric
The inverse relation R⁻¹ contains (b,a) whenever R contains (a,b). Consider any pair (a,b) in R∪R⁻¹. If it came from R, then (b,a) belongs to R⁻¹; if it came from R⁻¹, then (b,a) belongs to R. In both cases the reverse pair is in the same union, so R∪R⁻¹ is always symmetric. It need not be reflexive or transitive, and it is empty only in the special case R=∅.
Frequently asked questions
What is the correct answer to this question?
It is symmetric
Why is this the correct answer?
The inverse relation R⁻¹ contains (b,a) whenever R contains (a,b). Consider any pair (a,b) in R∪R⁻¹. If it came from R, then (b,a) belongs to R⁻¹; if it came from R⁻¹, then (b,a) belongs to R. In both cases the reverse pair is in the same union, so R∪R⁻¹ is always symmetric. It need not be reflexive or transitive, and it is empty only in the special case R=∅.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Symmetric relation.
