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Let P be the set of all ordered pairs (a, b) where a and b are...

Let P be the set of all ordered pairs (a, b) where a and b are real numbers. Let us define a two-place relation ≡ on P by (a, b) ≡ (c, d) if and only if a^2 − c^2 = 2b − 2d where (a, b) and (c, d) belong to P. Prove that ≡ is an equivalence relation on P. Draw a diagram on the X × Y plane of the equivalence class that contains the point (2, 2).

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