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On integers, (R={(a,b):a-b\equiv 1 \pmod{4}}). Is (R) symmetric?पूर्णांकों पर (R={(a,b):a-b\equiv 1 \pmod{4}}) है। क्या (R) सममित है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: No, because after reversing, (b-a\equiv 3 \pmod{4}) may occurनहीं, क्योंकि उलटने पर (b-a\equiv 3 \pmod{4}) हो सकता है
Step 1: If (a-b\equiv 1 \pmod{4}), then (b-a\equiv -1 \pmod{4}). Step 2: Since (-1\equiv 3 \pmod{4}), the reversed pair need not satisfy the original condition. Step 3: For subtraction-based congruence, check the sign carefully.चरण 1: यदि (a-b\equiv 1 \pmod{4}), तो (b-a\equiv -1 \pmod{4})। चरण 2: (-1\equiv 3 \pmod{4}), जो (1) के बराबर नहीं है। चरण 3: घटाव वाली सर्वांगसमता में उल्टी दिशा हमेशा वही शर्त नहीं देती।
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