यदि \(A=\{1,2,3\}\), तो (A) पर ऐसे संबंधों की संख्या क्या है जो प्रतिवर्ती और सममित दोनों हों?
If \(A=\{1,2,3\}\), how many relations on (A) are both reflexive and symmetric?
Explanation opens after your attempt
Correct Answer
A. \(2^3\)
Concept
Reflexivity makes the (3) diagonal pairs compulsory. For the remaining \(\binom{3}{2}=3\) off-diagonal pairs, each pair is either included together or excluded.
Why this answer is correct
The correct answer is A. \(2^3\). Reflexivity makes the (3) diagonal pairs compulsory. For the remaining \(\binom{3}{2}=3\) off-diagonal pairs, each pair is either included together or excluded.
Exam Tip
प्रतिवर्तीता से (3) विकर्ण युग्म अनिवार्य हैं। शेष \(\binom{3}{2}=3\) अविकर्ण जोड़ों में प्रत्येक जोड़ा साथ लिया या छोड़ा जाता है।
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