11. For any set X and any function f : X - X, the relation on X defined by $1 ~ x2 if f (x1) = f(x2) is always an equivalence relation. (a) * For the function f : R - R defined by f(x) = sin(x), describe [0] and describe [7]. (b) * What does it tell us about f if each equivalence class is a singleton (one element set)? (c) * For the function f : Z - Z defined by f(n) = n2, explain why the equivalence classes are {0}, {1, -1}, {2,-2}, {3,-3}, {4,-4},... Now give two more examples of functions with the same equivalence classes. (d) Give an example of a well-known function g : R - R where the corresponding equivalence classes are ..., [-3, -2), [-2, -1), [-1,0), [0, 1), [1, 2), [2, 3), [3, 4), ... Here [a, b) denotes the half-open interval {x |asx