समुच्चय (A) में (5) अवयव हैं। (A) पर प्रतिवर्ती और सममित दोनों संबंधों की संख्या कितनी होगी?
A set (A) has (5) elements. How many relations on (A) are both reflexive and symmetric?
Explanation opens after your attempt
Correct Answer
A. \(2^{10}\)
Concept
Reflexivity fixes the (5) diagonal pairs. Symmetry leaves only (\frac{5(5-1)}{2}=10) off-diagonal blocks free, so the answer is \(2^{10}\).
Why this answer is correct
The correct answer is A. \(2^{10}\). Reflexivity fixes the (5) diagonal pairs. Symmetry leaves only (\frac{5(5-1)}{2}=10) off-diagonal blocks free, so the answer is \(2^{10}\).
Exam Tip
प्रतिवर्ती होने से (5) diagonal pairs fixed हैं। सममिति में केवल (\frac{5(5-1)}{2}=10) off-diagonal blocks स्वतंत्र हैं, इसलिए \(2^{10}\)।
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