Let R = {(P,Q) | P and Q are at the same distance from the origin}

Question:

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

  1. $S=\left\{(x, y) \mid x^{2}+y^{2}=4\right\}$

  2. $S=\left\{(x, y) \mid x^{2}+y^{2}=1\right\}$

  3. $S=\left\{(x, y) \mid x^{2}+y^{2}=\sqrt{2}\right\}$

  4. $S=\left\{(x, y) \mid x^{2}+y^{2}=2\right\}$

Correct Option: , 4

Solution:

Equivalence class of $(1,-1)$ is a circle with centre

at $(0,0)$ and radius $=\sqrt{2}$

$\Rightarrow x^{2}+y^{2}=2$

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

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