Please explain how to solve part 1 and part 2 with explanation

Problem 2. This problem takes you through the formal definition of risk aversion / risk loving. Given a lottery P, let E (P) be the expected value of the lottery P. For example, if P = ($10, 0.5; $0, 0.5), then E(P) = 0.5 x 10 + 0.5 x 0 = 5 We say a person is . Risk averse if he chooses E (P) dollars for sure over the lottery P . Risk neutral if he is indifferent between E (P) dollars and the lottery P . Risk loving if he chooses the lottery P over E (P) dollars for sure. One way to measure "how" risk averse someone is is to use something called the Arrow- Pratt coefficient of risk aversion. Given a vNM utility u, the Arrow-Pratt coefficient is r (x) = (x) u' (I) (1) Ann has vNM utility uj (x) = z, Bob has utility u2 (x) = log (2x + 1) and Carl has utility u3 (x) = 23. Who is risk neutral, risk averse and risk loving? (2) Consider the lottery P again. Find the dollar amount r such that each person is indifferent between the lottery P and $x (x is the certainty equivalent of P)