Let R be a ring, and let R^R be the set of all functions mapping R into R. For∅, ψ ∈ R^R, define the sum∅ + ψ by (∅ + ψ)(r) = ∅(r) + ψ(r)  and the product ∅ . ψ by  (∅ · ψ)(r) = ∅(r)ψ(r) for r ∈ R. Note that · is not function composition. Show that (R^R,+,·) is a ring.