Show that the relation R in the set A of points in a plane given by R = {(P, Q): Distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all point related to a point $P \neq (0, 0)$ is the circle passing through P with the origin as centre.

Q. Let

A = {p, q, r}

. Which of the following is an equivalence relation in

A

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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 [1 mark]

The correct option is D S={(x,y):x2+y2=2}Let A(x,y) be an arbitrary point. Equivalence class of B(1,−1) is the set of those points A which are related to B(1,−1) such that OA=OB ⇒x2+y2=2

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

[1 mark]

The correct option is D $S = {(x, y) : x^{2} + y^{2} = 2}$
Let $A (x, y)$ be an arbitrary point.
Equivalence class of $B (1, - 1)$ is the set of those points $A$ which are related to $B (1, - 1)$ such that
$O A = O B$
$\Rightarrow x^{2} + y^{2} = 2$