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On (A={0,1,2,3,4,5}), (R={(a,b):a^2\equiv b \pmod{5}}). How many diagonal pairs are in (R)?समुच्चय (A={0,1,2,3,4,5}) पर (R={(a,b):a^2\equiv b \pmod{5}}) है। (R) में कितने विकर्ण युग्म हैं?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 33
Step 1: On the diagonal, put (b=a), giving (a^2\equiv a \pmod{5}). Step 2: This means (a(a-1)\equiv 0 \pmod{5}), so (a\equiv0) or (a\equiv1 \pmod{5}). Step 3: In the set, (0,1,5) work, so there are (3) diagonal pairs.चरण 1: विकर्ण पर (b=a) रखने से (a^2\equiv a \pmod{5}) मिलेगा। चरण 2: इससे (a(a-1)\equiv 0 \pmod{5}), इसलिए (a\equiv0) या (a\equiv1 \pmod{5})। चरण 3: दिए गए समुच्चय में (0,1,5) काम करते हैं, इसलिए (3) विकर्ण युग्म हैं।
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