Preferences Let R be a preference on A, with symmetric part I and asymmetric part P. (a) Prove that P is antisymmetric and transitive but not reflexive and not necessarily complete. (b) Prove that I...

Preferences

Let R be a preference on A, with symmetric part I and asymmetric part P.

(a) Prove that P is antisymmetric and transitive but not reflexive and not necessarily complete.

(b) Prove that I is reflexive and transitive but not necessarily complete and not necessarily antisymmetric.