2) From the original preference relation we can define two more relations as defined in class. Indifference: A B if and only if A B and BZ A. Strict preference: A

B if and only if A B and B A (i.e., B is not weakly preferred to A) [Note: If you're comfortable doing so, I highly suggest you give logical proofs, but for those of you new at this a careful intuitive explanation will suffice.] a) Which of our three axioms (Completeness, Reflexivity, Transitivity) are satisfied by the indifference relation, ~ ? b) Which of our three axioms are satisfied by the strict preference relation, > ?