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On (A={1,2,3,4,6}), (R={(a,b):\operatorname{lcm}(a,b)=6}). What type of relation is it?समुच्चय (A={1,2,3,4,6}) पर (R={(a,b):\operatorname{lcm}(a,b)=6}) है। यह संबंध कैसा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Symmetricसममित
Step 1: (\operatorname{lcm}(a,b)=\operatorname{lcm}(b,a)). Step 2: Therefore, if a pair has least common multiple (6), its reverse also has least common multiple (6). Step 3: Both LCM and GCD remain unchanged when the order is swapped.चरण 1: (\operatorname{lcm}(a,b)=\operatorname{lcm}(b,a)) होता है। चरण 2: इसलिए यदि किसी युग्म का लघुत्तम समापवर्त्य (6) है, तो उल्टे युग्म का भी (6) होगा। चरण 3: लघुत्तम समापवर्त्य और महत्तम समापवर्तक दोनों में क्रम बदलने से मान नहीं बदलता।
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