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On integers, (R={(a,b):a+b\equiv 0 \pmod{3}}). Which statement is correct for (R)?पूर्णांकों पर (R={(a,b):a+b\equiv 0 \pmod{3}}) है। (R) के लिए कौन सा कथन सही है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (R) is symmetric(R) सममित है
Step 1: The condition is (a+b\equiv 0 \pmod{3}). Step 2: Since (a+b=b+a), we also get (b+a\equiv 0 \pmod{3}). Step 3: Congruence conditions based on addition usually remain unchanged after swapping the order.चरण 1: शर्त (a+b\equiv 0 \pmod{3}) है। चरण 2: क्योंकि (a+b=b+a), इसलिए (b+a\equiv 0 \pmod{3}) भी होगा। चरण 3: जोड़ पर आधारित सर्वांगसमता में क्रम बदलने से शर्त नहीं बदलती।
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