Question: Let S = {1, 2, 3, 4}. Let F be the set of all functions f from S to S. Let R be the relation in F defined by

For any f, g ∈ F, fRg if and only if f (1) + f (2) = g (1) + g (2).

Prove that R is an equivalence relation in F.

I understand that to do this we must show that R is reflexive, symmetric and transitive. I only have problems to use the definitions of these 3 properties to make a real test.