यदि (R) और (S) दोनों (A) पर equivalence relations हैं, तो \(R\cap S\) के बारे में कौन सा कथन हमेशा सही है?
If (R) and (S) are both equivalence relations on (A), which statement about \(R\cap S\) is always true?
Explanation opens after your attempt
A. \(R\cap S\) भी equivalence relation है\(R\cap S\) is also an equivalence relation
Concept
The intersection retains common diagonal pairs, and symmetry and transitivity are also preserved. Hence the intersection of equivalence relations is again an equivalence relation.
Why this answer is correct
The correct answer is A. \(R\cap S\) भी equivalence relation है / \(R\cap S\) is also an equivalence relation. The intersection retains common diagonal pairs, and symmetry and transitivity are also preserved. Hence the intersection of equivalence relations is again an equivalence relation.
Exam Tip
Intersection में common diagonal pairs रहते हैं और symmetry तथा transitivity भी preserve होती हैं। इसलिए equivalence relations का intersection फिर equivalence relation होता है।
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