Let X CRX R. For any two bundles x = (x1, x) X and y (y,...

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Let X CRX R. For any two bundles x = (x1, x) X and y (y, y2) X define the relation as follows: 1 x L Y if and only if [x > y] or [x = y and x y]. x2 Y2]. (1) Assume the choice space is X = [0, 1] 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 [-1, 1]. Can this preference relationship be represented by a utility function? Show all details of your claim and its proof. Let X CRX R. For any two bundles x = (x1, x) X and y (y, y2) X define the relation as follows: 1 x L Y if and only if [x > y] or [x = y and x y]. x2 Y2]. (1) Assume the choice space is X = [0, 1] 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 [-1, 1]. Can this preference relationship be represented by a utility function? Show all details of your claim and its proof.