 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2022/discrete-mathematics-continuous-mathematics-and-probability/discrete-mathematics/3/c/i/solution

Write

q (x, y) = x^{2} + y^{2}

. Equality of

q

R

(x, y)

[(x, y)] = {(u, v) : u^{2} + v^{2} = x^{2} + y^{2}} .

For

(x, y) \neq = (0, 0)

this is the circle centred at the origin with radius

x^{2} + y^{2}

; the remaining equivalence class is the singleton

{(0, 0)}

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