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If a b c (if a is strictly preferred to be which is strictly preferred to c), then the definition of transitivity immediately tells that
If a b c (if a is strictly preferred to be which is strictly preferred to c), then the definition of transitivity immediately tells that a c must hold. Prove that transitivity in fact guarantees that a c (a is strictly preferred to c). (Hint: First prove that transitivity rules out a c and then show that a c is the only remaining possibility).
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