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If (A) has (n) elements, how many reflexive relations have exactly (n+2) ordered pairs?यदि (A) में (n) तत्व हैं, तो ऐसे प्रतिवर्ती संबंधों की संख्या क्या होगी जिनमें ठीक (n+2) युग्म हों?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\binom{n^2-n}{2})(\binom{n^2-n}{2})
Step 1: A reflexive relation must contain (n) diagonal pairs. Step 2: To have exactly (n+2) pairs, choose (2) non-diagonal pairs. Step 3: Since there are (n^2-n) non-diagonal pairs, the number is (\binom{n^2-n}{2}).चरण 1: प्रतिवर्ती संबंध में (n) विकर्ण युग्म अनिवार्य हैं। चरण 2: ठीक (n+2) युग्म चाहिए, इसलिए (2) अविकर्ण युग्म चुनने होंगे। चरण 3: अविकर्ण युग्म (n^2-n) हैं, अतः संख्या (\binom{n^2-n}{2}) है।
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