यदि relation (R) सममित और antisymmetric दोनों है, तो (R) में कौन से off-diagonal pairs हो सकते हैं?
If a relation (R) is both symmetric and antisymmetric, which off-diagonal pairs can occur in (R)?
Explanation opens after your attempt
Correct Answer
A. कोई भी नहींNone
Concept
If ((a,b)) with \(a\neq b\) occurs, symmetry forces ((b,a)), contradicting antisymmetry. Hence only diagonal pairs can occur.
Why this answer is correct
The correct answer is A. कोई भी नहीं / None. If ((a,b)) with \(a\neq b\) occurs, symmetry forces ((b,a)), contradicting antisymmetry. Hence only diagonal pairs can occur.
Exam Tip
यदि ((a,b)) और \(a\neq b\) हो, तो symmetry से ((b,a)) भी होगा, जो antisymmetry का विरोध करेगा। इसलिए केवल diagonal pairs संभव हैं।
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