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On (A={0,1,2,3,4}), (R={(a,b):a^2\equiv b^2 \pmod{5}}). How many total pairs are in (R)?(A={0,1,2,3,4}) पर (R={(a,b):a^2\equiv b^2 \pmod{5}}) है। (R) में कुल कितने युग्म हैं?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 99
Step 1: Square remainders form the groups ({0}), ({1,4}), and ({2,3}). Step 2: Pairs are formed between elements with the same square remainder. Step 3: Total pairs are (1^2+2^2+2^2=9).चरण 1: वर्ग शेषफलों से समूह ({0}), ({1,4}), और ({2,3}) बनते हैं। चरण 2: समान वर्ग शेषफल वाले तत्वों के बीच युग्म बनेंगे। चरण 3: कुल युग्म (1^2+2^2+2^2=9) होंगे।
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