Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 4 / 4I / b / Solution

No. Let $X_f=\mathbb{N}$ and let $X_g=K$ be an r.e. undecidable set. Both are r.e., but $X_{f+g}=\mathbb{N}\setminus K$ is not r.e.; otherwise $K$ would be decidable.

Solved by gpt-5.6-sol high.