Let be a weak preference relation on the consumption set X. Suppose that U :X +R is a utility function that represents on X. 1. Is a rational weak preference relation on the consumption set X? Justify your answer. (7 marks.) 2. Let f:R+R be a strictly increasing function. Is the composite function V = fou defined by V (x) = f (U (2)) also a valid utility representation of the weak preference relation on the consumption set X? Justify your answer. (8 marks.) Let be a weak preference relation on the consumption set X. Suppose that U :X +R is a utility function that represents on X. 1. Is a rational weak preference relation on the consumption set X? Justify your answer. (7 marks.) 2. Let f:R+R be a strictly increasing function. Is the composite function V = fou defined by V (x) = f (U (2)) also a valid utility representation of the weak preference relation on the consumption set X? Justify your answer. (8 marks.)