If Dawson prefers pizza to hamburgers and hamburgers to hot dogs, then if preferences are transitive

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If preferences are transitive and Dawson prefers pizza to hamburgers and hamburgers to hot dogs, it follows that she must also prefer pizza to hot dogs. This is because transitivity means that if A > B and B > C, then A > C. Therefore, if pizza is preferred to hamburgers and hamburgers are preferred to hot dogs, then pizza must be preferred to hot dogs. There is no option for Dawson to be indifferent among the three items or prefer hamburgers to pizza on some occasions because these would violate transitivity. Additionally, she cannot prefer hot dogs to pizza on some occasions because this would contradict her preference for hamburgers over hot dogs.

If Dawson Prefers Pizza to Hamburgers and Hamburgers to Hot