समुच्चय \(A=\{1,2,3\}\) पर empty relation \(R=\varnothing\) के बारे में कौन सा कथन सही है?
For \(A=\{1,2,3\}\), which statement is correct about the empty relation \(R=\varnothing\)?
Explanation opens after your attempt
A. यह सममित और संक्रामी है पर प्रतिवर्ती नहींIt is symmetric and transitive but not reflexive
Concept
The empty relation has no counterexample, so symmetry and transitivity are vacuously true. But \((1,1)\notin R\), so it is not reflexive.
Why this answer is correct
The correct answer is A. यह सममित और संक्रामी है पर प्रतिवर्ती नहीं / It is symmetric and transitive but not reflexive. The empty relation has no counterexample, so symmetry and transitivity are vacuously true. But \((1,1)\notin R\), so it is not reflexive.
Exam Tip
Empty relation में कोई counterexample नहीं, इसलिए symmetry और transitivity vacuously true हैं। पर \((1,1)\notin R\), इसलिए reflexive नहीं।
Login to save your score, XP, coins and progress.