Final answer:
The indifference and strict preference relations can be derived from a rational preference relation on a finite set. Examples include A ≽ B but not B ≽ A, A > B, A ≽ C, and B ≽ C.
Step-by-step explanation:
When considering a finite set X and a rational preference relation ∼ on X, we can derive the indifference and strict preference relations ≽ and >, respectively. For example, let's assume X is a set of three items: A, B, and C. If a person prefers item A to item B, we can denote it as A ≽ B. If the preference is strict, meaning the person strictly prefers A to B, we can denote it as A > B. Here are some examples: A ≽ B but not B ≽ A A > B A ≽ C B ≽ C