The answers to exercise marked [BB] can be found in the Back of the Book.Let A be a set an...

The answers to exercise marked [BB] can be found in the Back of the Book.

Let A be a set and let ƒ: A → A be a function. For x, y e A, define x ~ y if f(x) = f(y).

(a) Prove that ~ is an equivalence relation on A.

(b) For A = R and f(x) = [x], find the equivalence classes of 0, , and .

(c) Suppose A = (1, 2, 3, 4, 5, 6) and ƒ = {(1, 2), (2. 1), (3, 1), (4, 5), (5, 6), (6, 1). Find all equivalence classes.