I. in class, we defined a function f : n ? z by if n is even f(n)- if n is odd - 2 a) prove that f is a bijection. b) find a formula for the inverse function -, e n. b) let 2n denote the set of nonnegative even integers. what is f(2n)? c) let zk0 denote the set of nonnegative întegers. what is 2. prove that the union of two countable sets is countable. 3. use the previous exercise to show that the set of irrational numbers is uncountable