JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Sets Relations and Functions

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 :

Answer: (C)

Solution

The equivalence class of a point

(a, b)

under the relation

R

consists of all points at the same distance from the origin as

(a, b)

.

The distance of

(1, - 1)

from the origin is

1^{2} + (- 1)^{2} = 2

.

The equivalence class is the set of all points

(x, y)

such that

x^{2} + y^{2} = 2

, which gives

x^{2} + y^{2} = 2

.

Therefore,

S = {(x, y) ∣ x^{2} + y^{2} = 2}

JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Single correct option