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If (R={(1,1),(2,2),(3,3),(1,2)}) on (A={1,2,3}), is (R) antisymmetric?यदि (A={1,2,3}) पर (R={(1,1),(2,2),(3,3),(1,2)}), तो (R) प्रतिसममित है या नहीं?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Yesहाँ
Step 1: Antisymmetry fails when both ((a,b)) and ((b,a)) exist for distinct (a,b). Step 2: Here ((1,2)) is present but ((2,1)) is not. Step 3: So antisymmetry is not violated, and the relation is antisymmetric.चरण 1: प्रतिसममितता तब टूटती है जब अलग (a,b) के लिए दोनों ((a,b)) और ((b,a)) हों। चरण 2: यहां ((1,2)) है पर ((2,1)) नहीं है। चरण 3: इसलिए प्रतिसममितता नहीं टूटती और संबंध प्रतिसममित है।
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