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On (A={1,2,3,4,5,6,7}), (aRb) holds when (a) and (b) have the same divisibility status by (3) and the same divisibility status by (2). How many ordered pairs are in this relation?समुच्चय (A={1,2,3,4,5,6,7}) पर (aRb) तब है जब (a) और (b) दोनों (3) से विभाज्य होने की स्थिति और (2) से विभाज्य होने की स्थिति में समान हों। इस संबंध में कुल कितने क्रमित युग्म होंगे?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (15)(15)
Step 1: The classes are ({1,5,7}), ({2,4}), ({3}), and ({6}). Step 2: The number of ordered pairs is (3^2+2^2+1^2+1^2). Step 3: The total is (9+4+1+1=15).चरण 1: वर्ग ({1,5,7}), ({2,4}), ({3}), ({6}) बनते हैं। चरण 2: युग्मों की संख्या (3^2+2^2+1^2+1^2) होगी। चरण 3: कुल (9+4+1+1=15) युग्म होंगे।
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