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If (R) is symmetric on (A={1,2,3}) and contains exactly one diagonal pair and exactly two off-diagonal ordered pairs, how many such relations are possible?यदि (A={1,2,3}) पर (R) सममित है और (R) में ठीक एक विकर्ण युग्म तथा ठीक दो गैर-विकर्ण युग्म हैं, तो ऐसे संबंधों की संख्या कितनी होगी?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (9)(9)
Step 1: There are (3) ways to choose one diagonal pair. Step 2: Two off-diagonal ordered pairs mean one reverse-pair group; with (3) elements, there are (\binom{3}{2}=3) such groups. Step 3: Total possibilities are (3\cdot3=9).चरण 1: एक विकर्ण युग्म चुनने के (3) तरीके हैं। चरण 2: दो गैर-विकर्ण क्रमित युग्मों का अर्थ है एक उल्टा जोड़ी समूह; (3) अवयवों में ऐसे समूह (\binom{3}{2}=3) हैं। चरण 3: कुल तरीके (3\cdot3=9) होंगे।
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