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On (A={1,2,3,4,5}), (R={(a,b):a \equiv b+1 \pmod{2}}). Is (R) reflexive?समुच्चय (A={1,2,3,4,5}) पर (R={(a,b):a \equiv b+1 \pmod{2}}) है। (R) परावर्ती है या नहीं?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Noनहीं
Step 1: For reflexivity, put (b=a). Step 2: The condition becomes (a \equiv a+1 \pmod{2}), which means (0 \equiv 1 \pmod{2}), false. Step 3: Such shifted congruence conditions often fail for self-pairs.चरण 1: परावर्ती जाँच के लिए (b=a) रखें। चरण 2: शर्त (a \equiv a+1 \pmod{2}) बनेगी, जिसका अर्थ है (0 \equiv 1 \pmod{2}), यह असत्य है। चरण 3: ऐसी शर्त में स्वयं से संबंध अक्सर नहीं बनता।
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