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

Amira is painting a rectangular banner 2 1/4 yards wide. the banner will have a blue background. amira has enough paint to cover 1 1/2 square yards of the wall. the school colors are blue and yellow, so amira wants to add yellow rectangles on the left and right sides of the blue rectangle. the yellow rectangles will each be 3/4 yards wide and the same height as the blue rectangle. what will be the total area of the two yellow rectangles?