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On (A={1,2,3,4,5,6,7,8,9}), (aRb) holds when (a) and (b) have the same number of prime factors counted with repetition. Which is the equivalence class of (6)?समुच्चय (A={1,2,3,4,5,6,7,8,9}) पर (aRb) तब है जब (a) और (b) के अभाज्य गुणनखंडों की संख्या समान हो। (6) का तुल्यता वर्ग कौन सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: ({4,6,9})({4,6,9})
Step 1: (6=2\cdot3), so it has two prime factors with repetition. Step 2: (4=2^2) and (9=3^2) also have two prime factors. Step 3: Count repeated prime factors when the condition says so.चरण 1: (6=2\cdot3), इसलिए इसमें दो अभाज्य गुणनखंड हैं। चरण 2: (4=2^2) और (9=3^2) में भी दो अभाज्य गुणनखंड हैं। चरण 3: गुणनखंडों की संख्या गिनते समय पुनरावृत्ति को भी गिनना है।
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