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On (A={1,2,3}), (R={(1,1),(2,2),(1,2),(2,1),(2,3),(3,2)}). Which property is definitely present?समुच्चय (A={1,2,3}) पर (R={(1,1),(2,2),(1,2),(2,1),(2,3),(3,2)}) है। कौन-सा गुण निश्चित रूप से है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Symmetricसममित
Step 1: Both ((1,2)) and ((2,1)) are present. Step 2: Both ((2,3)) and ((3,2)) are present, and diagonal pairs are their own reverses. Step 3: Missing ((3,3)) prevents reflexivity, but not symmetry.चरण 1: ((1,2)) और ((2,1)) दोनों हैं। चरण 2: ((2,3)) और ((3,2)) दोनों हैं, तथा विकर्ण युग्म अपने उलटे स्वयं हैं। चरण 3: ((3,3)) न होने से प्रतिवर्तीता नहीं, पर सममितता बनी रहती है।
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