• Given a set $X$, a permutation of $X$ is a bijection $\sigma : X \longrightarrow X$. That is, it is a function with domain and codomain $X$ which is one to one and onto.
• Given a set $X$, the set $\mathrm{S}X$ is the set of all permutations of $X$.
Prove that, for any set $X$, $\mathrm{S}X$ is a group under function composition.
I understand the four properties it needs to prove that it's a group but I don't know how to apply it to this question.