= Solution
{c}
For a <singleton> $X$, the <symmetric group> contains only the <identity function>. For a two-element <set>, it contains the <identity function> and the <transposition> exchanging the two elements; the latter squares to the <identity function>. In both cases all elements <commute>, so the <group> is <Abelian>.
If $X$ contains three distinct elements $a,b,c$, define the <transpositions> $\sigma=(a\ b)$ and $\tau=(b\ c)$, fixing every other element of $X$. They are <bijections>, even when $X$ is infinite. With <function composition> read from right to left,
$$
(\sigma\circ\tau)(a)=b,\qquad (\tau\circ\sigma)(a)=c.
$$
Thus they do not <commute>, so the <symmetric group> is not <Abelian>. Since $X$ is nonempty, this proves
$$
\boxed{\operatorname{Sym}(X)\text{ is abelian}\quad\Longleftrightarrow\quad X\text{ is finite and }|X|\leq2.}
$$
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