The Alternating Group Is A Subgroup Of The Symmetric Group

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Problem 65C (optional) (The Alternating Group Is A Subgroup Of The Symmetric Group)

Let $n\in \mathbb{N}$. Prove that $A_n$ is a subgroup of $S_n$.

1. Do this using the problem The Subgroup Test - Subgroups Are Subsets That Are Closed Under Products And Taking Inverses.
2. Do this using the problem Finite Subgroup Test.

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