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On (A={1,2,3,4,5}), (R={(a,b):a+b\equiv0\pmod 3}). Which property does this relation satisfy?समुच्चय (A={1,2,3,4,5}) पर (R={(a,b):a+b\equiv0\pmod 3}) है। यह संबंध किस गुण को पूरा करता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: symmetric onlyकेवल सममित
Step 1: If (a+b\equiv0\pmod3), then (b+a\equiv0\pmod3), so it is symmetric. Step 2: ((1,1)) is absent because (1+1\equiv2\pmod3), so it is not reflexive. Step 3: (1R2) and (2R1) hold, but (1R1) fails, so it is not transitive.चरण 1: (a+b\equiv0\pmod3) होने पर (b+a\equiv0\pmod3), इसलिए सममित है। चरण 2: ((1,1)) नहीं है क्योंकि (1+1\equiv2\pmod3), इसलिए प्रतिवर्ती नहीं। चरण 3: (1R2) और (2R1) सही हैं, पर (1R1) गलत है, इसलिए संक्रामी नहीं।
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