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On real numbers, (aRb) iff (a-b\in\mathbb{Q}). What is the equivalence class of (\sqrt{2})?वास्तविक संख्याओं पर (aRb) तभी जब (a-b\in\mathbb{Q})। (\sqrt{2}) का समतुल्यता वर्ग कौन सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: ({\sqrt{2}+q:q\in\mathbb{Q}})({\sqrt{2}+q:q\in\mathbb{Q}})
Step 1: A number (x) related to (\sqrt{2}) must satisfy (x-\sqrt{2}\in\mathbb{Q}). Step 2: Hence (x=\sqrt{2}+q), where (q\in\mathbb{Q}). Step 3: Convert the defining condition directly into set-builder form.चरण 1: (\sqrt{2}) से संबंधित संख्या (x) के लिए (x-\sqrt{2}) परिमेय होना चाहिए। चरण 2: इसलिए (x=\sqrt{2}+q), जहां (q\in\mathbb{Q})। चरण 3: वर्ग लिखते समय शर्त को सीधे चल रूप में बदलें।
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