 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ii/paper-1/12g/d/i/solution

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

The total computable maps

n ⟼ 2 n, n ⟼ 2 n + 1

satisfy

n \in X ⟺ 2 n \in X \oplus Y, n \in Y ⟺ 2 n + 1 \in X \oplus Y .

Hence $X \leq_{m} X \oplus Y$ and $Y \leq_{m} X \oplus Y$ .

 New to topics? Read the docs here!