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

Use the following statements to write a compound statement for the conjunction or disjunction. then find its truth value. p: an isosceles triangle has two congruent sides. q: a right angle measures 90° r: four points are always coplanar. s: a decagon has 12 sides. a) a right angle measures 90° or an isosceles triangle has two congruent sides; true. b) a right angle measures 90° and an isosceles triangle has two congruent sides; true. c) a right angle measures 90° and an isosceles triangle does not have two congruent sides; false. d) a right angle measures 90° or an isosceles triangle does not have two congruent sides; true.