Solution
= Solution
A <many-one reduction> $A\leq_mB$ is a <total computable function> $f$ such that
$$
n\in A\quad\Longleftrightarrow\quad f(n)\in B.
$$
If $B$ is a <computably enumerable set>, compute $f(n)$ and run a semidecision procedure for $B$ on that value. It halts exactly when $f(n)\in B$, equivalently exactly when $n\in A$. \b[Therefore $A$ is computably enumerable.]