 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-2/2g/iv/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

False. The coordinate axes

A = R \times {0}, B = {0} \times R

are both closed nowhere dense subsets of

R^{2}

, but every

(x, y)

(x, 0) + (0, y)

, so

A + B = R^{2},

which is not meagre by the Baire category theorem.

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