10 8. Define the relation R on Z by aRb if and only if a2 + 2b2 = 0 (mod 3).а. (Prove that R is an equivalence relation.Since R is an equivalence relation of Z, it will also be an equivalence relation on A =b.{0,1,2,3,4,5,6}. When R isan equivalence relation on A, what are the distinct equivalence classes?Page 1 has 66 pointsPage 2 has 47 points9. Suppose f:[2, ) → [0, ∞) is defined by f(x)Prove that f is a bijection.= Vx - 2.а. (b.What is f-'(x)?10. Convertа.., 7860, to decimalb.1854 to base 5.11. (a. In how many ways can they finish?b. The top five runners win medals. In how many ways can these medals be awarded?c. The top five runners win medals. In how many ways can these medals be awarded if Jesse and Owen each get anSixteen runners are in a race. Answer each of the following, but do not calculate the final answer.award?d. The top five runners move onto finals. In how many ways can five runners be selected to move on to finals?A pizzeria offers 20 different toppings. Answer each of the following, but do not calculate the final answer.12. (a. How many pizzas are there with any number of toppings, no double-toppings allowed.b. How many 8-topping pizzas are there?c. How many 6-topping pizzas are there if we are not allowed to have both pepperoni and sausage?d. BONUSHow many 4-topping pizzas are there if doubling is allowed. For example, you could have a sausage,bacon, ana double-onion pizza. Note that when toppings are doubled, it counts as two toppings.

Name: 10 8. Define the relation R on Z by aRb if and only if a2 + 2b2 = 0 (m
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Description: 10 8. Define the relation R on Z by aRb if and only if a2 + 2b2 = 0 (mod 3).а. (Prove that R is an equivalence relation.Since R is an equivalence relation of Z, it will also be an equivalence relation on A =b.{0,1,2,3,4,5,6}. When R isan equivalence