Solution
= Solution
\b[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.
= Solution
\b[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.