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NDA 2025 Maths · Mathematics · Sets, Relations and Functions · medium

On mathbbR, the relation R is defined by xRy if and only if |x|=|y|. The equivalence class of -4 is

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On R\mathbb{R}, the relation RR is defined by xRyxRy if and only if ∣x∣=∣y∣|x|=|y|. The equivalence class of −4-4 is
  1. A. {−4,4}\{-4,4\}
  2. B. {4}\{4\}
  3. C. {−4}\{-4\}
  4. D. R\mathbb{R}
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Answer: (A) {−4,4}\{-4,4\}

The relation is reflexive, symmetric and transitive, so it is an equivalence relation. The class of −4-4 contains all yy with ∣y∣=∣−4∣=4|y|=|-4|=4, namely y=4y=4 and y=−4y=-4. Hence the class is {−4,4}\{-4,4\}.
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Original question written in the NDA 2025 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake