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On (A={1,2,3,4}), (R) is reflexive and has exactly (9) pairs. How many such relations are possible?समुच्चय (A={1,2,3,4}) पर (R) प्रतिवर्ती है और (R) में ठीक (9) युग्म हैं। ऐसे संबंधों की संख्या क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\binom{12}{5})(\binom{12}{5})
Step 1: The four diagonal pairs are compulsory. Step 2: To have (9) total pairs, choose (5) non-diagonal pairs. Step 3: Choosing (5) from (12) non-diagonal pairs gives (\binom{12}{5}).चरण 1: चार विकर्ण युग्म अनिवार्य हैं। चरण 2: कुल (9) युग्म के लिए (5) अविकर्ण युग्म चुनने होंगे। चरण 3: (12) अविकर्ण युग्मों में से (5) चुनने के तरीके (\binom{12}{5}) हैं।
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