Exercise 9: This is a formal proof. Remember An+2 is the set of all even permutations of {1,2,3,...,n,n+1,n+2} and Sn is the set of all permutations (both even and odd) of {1,2,3,....,n}. There are a couple of ways to prove this result. One approach involves finding a function f from Sn to An+2 and showing this function is an isomorphism. As a hint for this approach, consider the transposition a = (n+1,n+2) which swaps the last two numbers in the set but leaves the first n numbers fixed.

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