Please be noticed it's about the lexicographical order. And the internal is a very important point. If it can be represented by utility, you need use a function to show the relation. Please answer in detail

Question 1 Let X C R x R. For any two bundles m : ($1,952) E X and y : (3/1, 3/2) E X dene the relation 5L as follows: m j]; y if and only if [351 > yll or [$1 : yl and $2 g ml. (1) Assume the choice space is X : [0, l] 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