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