THEOREM 1.] Exists!\" oft: Reol-Huedi'uncon Representing the Preference Relation 5 If the binary relation : is complete, tramltire. cmtimrous. and strictly tmnototlt'rr. there exists a continuous real-valued function. u: 111; R. which represents Z: . Suppose the binary preference relation is not continuous but holds all other properties mentioned in Theorem 1.1 {Advanced Mlcroeconomic Theory, lehle and Reny). How would the utility function look like? Can you offer an example of a preference relation to illustrate this utility function? Suppose the binary preference relation is not complete but holds all other properties mentioned in Theorem 1.1 (Advanced Microeconomtc Theory, lehle and Benny). How would the utility function look like? Can you offer an example of a preference relation to illustrate this utility function