Question:
Let $\mathrm{R}=\{\mathrm{P}, \mathrm{Q}) \mid \mathrm{P}$ and $\mathrm{Q}$ are at the same distance from the origin $\}$ be a relation, then the equivalence class of $(1,-1)$ is the set:
Correct Option: , 4
Solution:
$\mathrm{P}(\mathrm{a}, \mathrm{b}), \mathrm{Q}(\mathrm{c}, \mathrm{d}), \mathrm{PO}=\mathrm{QO}$
$\Rightarrow a^{2}+b^{2}=c^{2}+d^{2}$
$\mathrm{R}(\mathrm{x}, \mathrm{y}) \quad \mathrm{s}=(1,-1) \Rightarrow \mathrm{RO}=\mathrm{SO}$
( $\because$ equivalence class)
$x^{2}+y^{2}=2$
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