Olson likes strong coffee, the stronger the better. But he can€™t distinguish small differences. Over the years, Mrs. Olson has discovered that if she changes the amount of coffee by more than one teaspoon in her six-cup pot, Olson can tell that she did it. But he 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 Olson prefers cup A to cup B. Let us write A _ B if Olson either prefers A to B, or can€™t tell the difference between them. Let us write A ~ B if Olson can€™t tell the difference between cups A and B. Suppose that Olson is offered cups A, B, and C all brewed in the Olsons€™ 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 C was brewed using 15.5 teaspoons of coffee in the pot. For each of the following expressions determine whether it is true of false.

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(a) A - B. (b) B - A. (c) B - C. (d) A - C. (e) C - A. (f)A B. (g) B A. (h) B C. 1) A C. 6) C =A. (k) A > B. ) в А. (m) B > C. (n) A > C. (0) C > A. (p) Is Olson's "at-least-as-good-as" relation, , transitive? (q) Is Olson's “can't-tell-the-difference" relation, ~, са transitive? (1) Is Olson's "better-than" relation, >, transitive.