समुच्चय \(A=\{1,2,3\}\) पर \(R=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}\) है। क्या (R) antisymmetric है?
On \(A=\{1,2,3\}\), \(R=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}\). Is (R) antisymmetric?
Explanation opens after your attempt
Correct Answer
A. हाँ, क्योंकि कोई distinct reverse pair साथ में नहीं हैYes, because no distinct reverse pair appears together
Concept
Antisymmetry is not affected by diagonal pairs. It fails only when ((a,b)) and ((b,a)) both occur for \(a\neq b\).
Why this answer is correct
The correct answer is A. हाँ, क्योंकि कोई distinct reverse pair साथ में नहीं है / Yes, because no distinct reverse pair appears together. Antisymmetry is not affected by diagonal pairs. It fails only when ((a,b)) and ((b,a)) both occur for \(a\neq b\).
Exam Tip
Antisymmetry को diagonal pairs से समस्या नहीं होती। समस्या तभी होती है जब \(a\neq b\) पर ((a,b)) और ((b,a)) दोनों हों।
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