= Solution
{c}
The <function composition> of two <bijections> $f,g:X\to X$ is a <bijection>, with <inverse function> $(f\circ g)^{-1}=g^{-1}\circ f^{-1}$. Thus <function composition> is a <binary operation> on $\operatorname{Sym}(X)$. It is <associative>, since both $(f\circ g)\circ h$ and $f\circ(g\circ h)$ send $x$ to $f(g(h(x)))$.
The <identity function> $\operatorname{id}_X$ is a <bijection> and satisfies $f\circ\operatorname{id}_X=\operatorname{id}_X\circ f=f$. Every <bijection> $f$ has an <inverse function> $f^{-1}:X\to X$, itself a <bijection>, satisfying $f\circ f^{-1}=f^{-1}\circ f=\operatorname{id}_X$. These verify all <group axioms>, so \b[$\operatorname{Sym}(X)$ is a <group>], the <symmetric group> of $X$.
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