Let A = R R . A relation R is defined on A by : (x₁, y₁) R (x₂, y₂) x₁^2 - y₁^2 = x₂^2 - y₂^2 Statement I : R is an equivalence relation. Statement II : The equivalence class of the point (2, 2) under the relation R represents a rectangular hyperbola. In the light of the above statements, choose the correct answer from the options given below :

Step-by-step solution

For Statement I : Reflexivity: (x, y) R (x, y) x^2 - y^2 = x^2 - y^2 , which is true. Symmetry: (x₁, y₁) R (x₂, y₂) x₁^2 - y₁^2 = x₂^2 - y₂^2 x₂^2 - y₂^2 = x₁^2 - y₁^2 (x₂, y₂) R (x₁, y₁) , which is true. Transitivity: (x₁, y₁) R (x₂, y₂) and (x₂, y₂) R (x₃, y₃) x₁^2 - y₁^2 = x₂^2 - y₂^2 and x₂^2 - y₂^2 = x₃^2 - y₃^2 x₁^2 - y₁^2 = x₃^2 - y₃^2 (x₁, y₁) R (x₃, y₃) , which is true. Thus, R is an equivalence relation. Statement I is true. For Statement II : The equivalence class of (2, 2) is the set of all points (x, y