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On the set of real numbers, relation (R) is defined by (aRb) if and only if (a-b>0). Is (R) symmetric?वास्तविक संख्याओं के समुच्चय पर संबंध (R) इस प्रकार है: (aRb) तभी जब (a-b>0)। क्या (R) सममित है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: No, because (a>b) does not imply (b>a)नहीं, क्योंकि (a>b) से (b>a) नहीं होता
Step 1: (a-b>0) means (a>b). Step 2: If (a>b), then generally (b>a) is false, so the reversed pair does not satisfy the condition. Step 3: In inequality-based relations, the reverse direction often fails.चरण 1: (a-b>0) का अर्थ है (a>b)। चरण 2: यदि (a>b) है, तो सामान्यतः (b>a) नहीं हो सकता, इसलिए उल्टा युग्म शर्त पूरी नहीं करता। चरण 3: असमिका वाले संबंधों में उल्टी दिशा अक्सर गलत हो जाती है।
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