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Let X be any set and let (G, ·) be a group. Let homset(X, G) be...

Let X be any set and let (G, ·) be a group. Let homset(X, G) be the set of all functions with domain X and codomain G. Prove that (homset(X, G), ∗), where (f ∗ g)(x) := f(x) · g(x), is a group.

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