A decision-maker's preferences over the set X={a,b,c} are represented by the payoff function u:XR for which u(a)=4,u(b)=1,andu(c)=4. Assume that this agent is rational (that is, he always chooses alternatives that maximize his payoffs). Write down this agent's choices from each subset of X (and note that by doing this, you are constructing a choice rule). Now check if these choices satisfy Sen's properties and