Question

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

• A. S=\left\\{(x, y) | x^{2}+y^{2}=4\right\\}
• B. S =\left\\{( x , y )| x ^{2}+ y ^{2}=1\right\\}
• C. S =\left\\{( x , y ) | x ^{2}+ y ^{2}=\sqrt{2}\right\\}
• D. S =\left\\{( x , y ) \mid x ^{2}+ y ^{2}=2\right\\}

Answer 1

Answer: (D)

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

Answer 2

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\\}