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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) S = {(x,y) | x^2 + y^2 = 4} (2) S = {(x,y) | x^2 + y^2 = 1} (3) S = {(x,y) | x^2 + y^2 = √2} (4) S = {(x,y) | x^2 + y^2 = 2}

1. S = {(x,y) | x^2 + y^2 = 4}
2. S = {(x,y) | x^2 + y^2 = 1}
3. S = {(x,y) | x^2 + y^2 = √2}
4. S = {(x,y) | x^2 + y^2 = 2}

Correct answer: S = {(x,y) | x^2 + y^2 = 2}

Solution

The correct option describes the set of points that are at the same distance from the origin as the point (1, -1), which has a distance of √2 from the origin. The equation x² + y² = 2 corresponds to this distance, confirming that the equivalence class includes all points equidistant from the origin.

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