(a) Let f be a function from A to B. Define the relation T on A by x T y iff f (x) =...

(a) Let f be a function from A to B. Define the relation T on A by x T y iff f (x) = f (y).

Prove that T is an equivalence relation on A.

(b) In the case when describe the equivalence class of 0; of 2; of 4.

(c) In the case when is the cosine function, describe the equivalence class of 0; of π/2; π/4.