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Homework answers / question archive / Olivia likes strong coffee, the stronger the better
Olivia likes strong coffee, the stronger the better. But she cannot distinguish small differences. Over the years, her boyfriend, Oliver, has discovered that if he changes the amount of coffee by more than one teaspoon in their six-cup pot, Olivia can tell that he did. But she cannot distinguish differences smaller than one teaspoon per pot. Where A and B are two different cups of coffee, let us write A B if Olivia prefers cup A to cup B. Let us write A2B (sorry, my software doesn't have the symbol for weak preference) if Olivia either prefers A to B. or cannot tell the difference between the two cups. Let us write A - B if Olivia cannot tell the difference between cup A and cup B. Suppose that Olivia is offered three cups, A, B, and C, all brewed in Olivia and Oliver's six-cup pot . Cup A was brewed using 14 teaspoons of coffee in the pot. Cup B was brewed using 14.75 teaspoons of coffee in the pot and cup was brewed using 15.5 teaspoons of coffee in the pot. a) Is Olivia's at least-as-good-as relation, 2, transitive? b) Is Olivia's cannot-tell-the-difference relation, -, transitive? c) Is Olivia's better than relation, transitive?
