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On real numbers, (aRb) iff (a-b\in\mathbb{Z}). What is the equivalence class of (\frac{1}{2})?वास्तविक संख्याओं पर (aRb) तभी जब (a-b\in\mathbb{Z})। (\frac{1}{2}) का समतुल्यता वर्ग कौन सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: ({\frac{1}{2}+n:n\in\mathbb{Z}})({\frac{1}{2}+n:n\in\mathbb{Z}})
Step 1: A number (x) must satisfy (x-\frac{1}{2}\in\mathbb{Z}). Step 2: Hence (x=\frac{1}{2}+n), where (n\in\mathbb{Z}). Step 3: To write the class, add all allowed integer differences to the representative.चरण 1: किसी (x) के लिए (x-\frac{1}{2}) पूर्णांक होना चाहिए। चरण 2: इसलिए (x=\frac{1}{2}+n), जहां (n\in\mathbb{Z})। चरण 3: वर्ग लिखते समय प्रतिनिधि में अनुमत पूर्णांक अंतर जोड़ें।
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