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On (A={1,2,3,4,5,6,7,8}), how many ordered pairs are in the relation defined by (\gcd(a,8)=\gcd(b,8))?समुच्चय (A={1,2,3,4,5,6,7,8}) पर (\gcd(a,8)=\gcd(b,8)) से बने संबंध में कुल कितने क्रमित युग्म होंगे?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (22)(22)
Step 1: The classes are ({1,3,5,7},{2,6},{4},{8}). Step 2: The number of pairs is (4^2+2^2+1^2+1^2). Step 3: The total is (16+4+1+1=22).चरण 1: वर्ग ({1,3,5,7},{2,6},{4},{8}) बनते हैं। चरण 2: युग्मों की संख्या (4^2+2^2+1^2+1^2) होगी। चरण 3: कुल (16+4+1+1=22) युग्म होंगे।
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