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On (A={1,2,3,4,5,6,7}), (aRb) if (a-b) is divisible by (2). What are the equivalence classes of (R)?समुच्चय (A={1,2,3,4,5,6,7}) पर (aRb) तभी जब (a-b) (2) से विभाज्य हो। (R) के तुल्यता वर्ग कौन से हैं?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: ({1,3,5,7},{2,4,6})({1,3,5,7},{2,4,6})
Step 1: Divisibility of (a-b) by (2) means the numbers have the same parity. Step 2: Odd elements form ({1,3,5,7}), and even elements form ({2,4,6}). Step 3: For parity relations, separate odd and even elements first.चरण 1: (a-b) का (2) से विभाज्य होना समान समता दिखाता है। चरण 2: विषम अवयव ({1,3,5,7}) और सम अवयव ({2,4,6}) अलग वर्ग बनाते हैं। चरण 3: समता के प्रश्नों में पहले सम और विषम छांटें।
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