Jane prefers a to b, b to c, and c to a. Based on this information, what properties are violated by Jane's preferences (only one answer is correct)?

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Answer:

Since Jane prefers a to b and b to c, then she must find a at least as good as b and b at least as good as c. Transitivity would imply that a is at least as good as c. But she prefers c to a, then a cannot be at least as good as c. So jane's statements violate transitivity. Completeness is satisfied because between any to alternatives one is at least as good as the other.