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On (A={1,2,3,4,5,6,7,8,9}), (aRb) holds when (\gcd(a,9)=\gcd(b,9)). How many ordered pairs are in the relation?समुच्चय (A={1,2,3,4,5,6,7,8,9}) पर (aRb) तब है जब (\gcd(a,9)=\gcd(b,9))। कुल कितने क्रमित युग्म संबंध में होंगे?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (41)(41)
Step 1: The classes are ({1,2,4,5,7,8}), ({3,6}), and ({9}). Step 2: The pair count is (6^2+2^2+1^2). Step 3: Thus the total is (36+4+1=41).चरण 1: वर्ग ({1,2,4,5,7,8}), ({3,6}) और ({9}) बनते हैं। चरण 2: युग्मों की संख्या (6^2+2^2+1^2) होगी। चरण 3: कुल (36+4+1=41) युग्म मिलते हैं।
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