The answers to exercise marked [BB] can be found in the Back of the Book.
Let S be a set containing the number 5. Let A = {ƒ: S → S}be the set of all functions S → S. For f, g ∈ A, define ~ g if f(5) = g(5).
(a) Prove that ~ defines an equivalence relation on A.
(b) Find the equivalence class of ƒ = {(5, a), (a, b), (b, b)} in the case S = {5, a, b}.
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