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