Suppose a function f : a → b is given. define a relation ∼ on a as follows: a1 ∼ a2 ⇐⇒ f(a1) = f(a2) (a) prove that ∼ is an equivalence relation on a. since ∼ is an equivalence relation, it induces a partition of a into equivalence classes. describe these equivalence classes in each of the following cases. (b) a is the set of all solid-color cars, b is the set of all colors, f(x) is the color of x. (c) a = b = r, f(x) = x2