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(Solved): 2. Let \( R \) be the Equivalence relation defined on \( \mathbb{R} \) by : \ ...
![2. Let \( R \) be the Equivalence relation defined on \( \mathbb{R} \) by :
\[
x R y \Leftrightarrow x^{2}-x=y^{2}-y
\]
(a) D](https://media.cheggcdn.com/media/537/5376c320-8d09-4c8d-ae6d-a74c93aadf66/phphs0EtC)
2. Let \( R \) be the Equivalence relation defined on \( \mathbb{R} \) by : \[ x R y \Leftrightarrow x^{2}-x=y^{2}-y \] (a) Determine \( \overline{2}, \overline{0} \). (b) Discuss the number of elements of \( \bar{x}, x \in \mathbb{R} \).