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On (A={1,2,3,4}), relation (R={(a,b):a-b\text{ is divisible by }2}) is given. Choose the correct option for (R).समुच्चय (A={1,2,3,4}) पर संबंध (R={(a,b):a-b\text{ is divisible by }2}) दिया है। (R) के लिए सही विकल्प चुनिए।
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Symmetricसममित है
Step 1: If (a-b) is divisible by (2), then (b-a=-(a-b)) is also divisible by (2). Step 2: Thus, each pair has its reverse pair. Step 3: In divisibility-based relations, a negative sign does not break symmetry.चरण 1: यदि (a-b) संख्या (2) से विभाज्य है, तो (b-a=-(a-b)) भी (2) से विभाज्य होगा। चरण 2: इसलिए ((a,b)) के साथ ((b,a)) भी संबंध में होगा। चरण 3: विभाज्यता में ऋण चिह्न सममिति को नहीं बिगाड़ता।
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