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If (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) on (A={1,2,3}), why is (R) not antisymmetric?यदि (A={1,2,3}) पर (R={(1,1),(2,2),(3,3),(1,2),(2,1)}), तो (R) प्रतिसममित क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because ((1,2)) and ((2,1)) are both present while (1\ne2)क्योंकि (1\ne2) होते हुए ((1,2)) और ((2,1)) दोनों हैं
Step 1: In antisymmetry, pairs in both directions should not occur between distinct elements. Step 2: Here (1) and (2) are distinct, yet both ((1,2)) and ((2,1)) are present. Step 3: Therefore, antisymmetry fails.चरण 1: प्रतिसममितता में अलग तत्वों के बीच दोनों दिशाओं के युग्म नहीं होने चाहिए। चरण 2: यहां (1) और (2) अलग हैं फिर भी ((1,2)) और ((2,1)) दोनों हैं। चरण 3: इसी कारण प्रतिसममितता टूट जाती है।
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