वास्तविक संख्याओं पर (aRb) तब और केवल तब जब \(a-b\in\mathbb{Q}\)। \([\sqrt{2}]\) का सही रूप कौन सा है?
On real numbers, (aRb) if and only if \(a-b\in\mathbb{Q}\). Which is the correct form of \([\sqrt{2}]\)?
Explanation opens after your attempt
Correct Answer
A. \({\sqrt{2}+q:q\in\mathbb{Q}}\)
Concept
\([\sqrt{2}]\) contains all (x) such that \(x-\sqrt{2}\in\mathbb{Q}\). Hence \(x=\sqrt{2}+q\) where \(q\in\mathbb{Q}\).
Why this answer is correct
The correct answer is A. \({\sqrt{2}+q:q\in\mathbb{Q}}\). \([\sqrt{2}]\) contains all (x) such that \(x-\sqrt{2}\in\mathbb{Q}\). Hence \(x=\sqrt{2}+q\) where \(q\in\mathbb{Q}\).
Exam Tip
\([\sqrt{2}]\) में वे सभी (x) हैं जिनके लिए \(x-\sqrt{2}\in\mathbb{Q}\)। इसलिए \(x=\sqrt{2}+q\) जहां \(q\in\mathbb{Q}\)।
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