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If (A={1,2,3,4,5}) and (R={(a,b):a^2+b^2<2ab}), is (R) reflexive?यदि (A={1,2,3,4,5}) और (R={(a,b):a^2+b^2<2ab}) है, तो (R) प्रतिवर्ती है या नहीं?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Noनहीं
Step 1: On the diagonal, put (a=b), giving (a^2+a^2<2a^2). Step 2: This becomes (2a^2<2a^2), which is false. Step 3: No diagonal pair satisfies the condition, so the relation is not reflexive.चरण 1: विकर्ण पर (a=b) रखने से (a^2+a^2<2a^2) मिलेगा। चरण 2: यह (2a^2<2a^2) है, जो असत्य है। चरण 3: कोई विकर्ण युग्म शर्त पूरी नहीं करता, इसलिए संबंध प्रतिवर्ती नहीं है।
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