Question 1 (30 marks). Consider the 3 element set X = {:L',y,z} with x, y, 2 all distinct, that is, not equal to each other. (1) How many elements are there in X X X? (2 marks) (2) Give an example of a binary relation R on the set X that is transitive and complete by explicitly listing the elements of R. (4 marks) Now, let the collection of budget sets B consist of all 1, 2, 3 element subsets of X. Consider the following choice correspondence: for each one element budget set the choice is, as it must be, that budget set, and (3) Does the given choice correspondence satisfy the weak axiom of revealed preference? (2 marks) (4) Show why or why not. (3 marks) (5) For the given choice correspondence nd the revealed (weak) pref- erence relation :3. Describe this preference relation by explicitly listing all the pairs (p, q) for which p :3 q. (5 marks) (6) Is the preference relation you found in the previous part transitive and complete? Show why your answer is correct. (4 marks) (7) Find the revealed strict preference relation >-R that corresponds to the weak preference relation that you found in part (5), that is, the relation >R that is dened by p >-R q if and only if p :R q and not q :R 1). Again describe this preference relation by explicitly listing all the pairs (19, q) for which p >R