Problem 3. Rationality of preferences [BONUS POINTS, OPTIONAL] Use the basic prop erties of preferences to prove the following statements: I if t is rational, then m is transitive, that is, cc m y and y m 2 implies a: N z o if >_- is rational, then: if a: > y >_- 2 then m > z. o if t is rational, then i has the reexive property, that is, a: >_- a: for all :3