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(D) The relation $R$ is defined as the set of all points $(P, Q)$ such that the distance of $P$ from the origin is equal to the distance of $Q$ from t

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$S = \{( x , y ) \mid x ^{2}+ y ^{2}=2\}$

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(D) The relation $R$ is defined as the set of all points $(P, Q)$ such that the distance of $P$ from the origin is equal to the distance of $Q$ from the origin.The equivalence class of a point $(x_0, y_0)$ is the set of all points $(x, y)$ such that the distance of $(x, y)$ from the origin is equal to the distance of $(x_0, y_0)$ from the origin.The distance of the point $(1, -1)$ from the origin $(0, 0)$ is given by $\sqrt{1^2 + (-1)^2} = \sqrt{1 + 1} = \sqrt{2}$.Therefore,the equivalence class of $(1, -1)$ consists of all points $(x, y)$ such that $\sqrt{x^2 + y^2} = \sqrt{2}$.Squaring both sides,we get $x^2 + y^2 = 2$.Thus,the equivalence class is the set $S = \{(x, y) \mid x^2 + y^2 = 2\}$.

Let $R = \{( P , Q ) \mid P \text{ and } Q \text{ are at the same distance from the origin} \}$ be a relation. Then the equivalence class of $(1, -1)$ is the set:

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