Prove theorem The Composition Of Permutations Is A Permutation. As some reminders, you may use the following facts that you proved in either Math 301 or Math 340. You may use these facts without proof.
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\begin{problem}
Prove theorem [[Theorem:The Composition Of Permutations Is A Permutation]]).
As some reminders, you may use the following facts that you proved in either Math 301 or Math 340. You may use these facts without proof.
\begin{itemize}
\item The composition of two injective functions is injective.
\item The composition of two surjective functions is surjective.
\item A function is a bijection if it is both injective (1 to 1) and surjective (onto). Hence, the composition of two bijective functions is a bijection.
\item You might find induction helps you get from a composition of two bijective functions is bijective to the composition of $n$ bijective functions is bijective.
\\end{itemize}
end{problem}