वास्तविक संख्याओं के समुच्चय \(\mathbb{R}\) पर (aRb) तभी जब \(a-b\in\mathbb{Z}\)। (R) की प्रकृति क्या है?
On the set of real numbers \(\mathbb{R}\), (aRb) if and only if \(a-b\in\mathbb{Z}\). What is the nature of (R)?
Explanation opens after your attempt
Correct Answer
A. तुल्यता संबंधEquivalence relation
Concept
Since \(a-a=0\in\mathbb{Z}\), \(a-b\in\mathbb{Z}\) implies \(b-a\in\mathbb{Z}\), and the sum of integers is an integer. Hence it is an equivalence relation.
Why this answer is correct
The correct answer is A. तुल्यता संबंध / Equivalence relation. Since \(a-a=0\in\mathbb{Z}\), \(a-b\in\mathbb{Z}\) implies \(b-a\in\mathbb{Z}\), and the sum of integers is an integer. Hence it is an equivalence relation.
Exam Tip
\(a-a=0\in\mathbb{Z}\), \(a-b\in\mathbb{Z}\) से \(b-a\in\mathbb{Z}\), और पूर्णांकों का योग पूर्णांक है। इसलिए यह तुल्यता संबंध है।
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