Please be noticed it's about the lexicographical order. If it can be represented by utility, you need use a function to show the relation.

Question 1 Let X C R X R. For any two bundles r : ($1,952) E X and y : (y1,y2) E X dene the relation jL as follows: x j]; y if and only if [351 > 3/1] or [$1 : 3/1 and 302 g 3/2]. (1) Assume the choice space is X : [0, 1] x Q. Can this preference relationship be represented by a utility function? Show all details of your claim and its proof. (2) Assume the choice space is X : N X [1, 1]. Can this preference relationship be represented by a utility function? Show all details of your claim and its proof