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If (R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3),(3,1)}) on (A={1,2,3}), which property definitely fails?यदि (A={1,2,3}) पर (R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3),(3,1)}), तो कौन सा गुण निश्चित रूप से टूटता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Antisymmetryप्रतिसममितता
Step 1: All self-pairs are present, so reflexivity does not fail. Step 2: Both ((1,3)) and ((3,1)) are present while (1\ne3). Step 3: This definitely breaks antisymmetry.चरण 1: सभी स्वयं युग्म मौजूद हैं, इसलिए स्वपरकता नहीं टूटती। चरण 2: ((1,3)) और ((3,1)) दोनों हैं जबकि (1\ne3)। चरण 3: यह प्रतिसममितता को निश्चित रूप से तोड़ता है।
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