1. Let the list of consequences be C : (Lg-1111:6338:Fusiliers). A simple lottery is a probability distrlbutlon over C, that 1s1 a pair of numbers (p8, pF) such that p8: p S 1 and 103+ pF 2 1. Suppose that a decisionmaker has a rational and continuous preference relation over such lotteries. Suppose further that is such that @3: PF) (pg, 10%) if and only if pg 2 39%. (a) Show that the decisionmaker"s preferences satisfy the independence axiom. (1)) Provide a function "u- : C > R such that is represented by a yon Neurnann Morgenstern utility function U over lotteries that has expected utility form with Bernoulli utility function u