Ward Cleaver likes strong coffee, the stronger the better, but Ward can't distinguish small differences. Over the years, June (Ward's homemaker wife) has determined that if she changes the amount of coffee by more than one teaspoon in their six-cup pot, Ward can tell that she did it. But Ward cannot distinguish differences smaller than one teaspoon per pot.

Where A and B are two different cups of coffee:

Let us write (A strict preference to B)if Ward prefers cup A to cup B;

Let us write(A weak preference to B)if Ward either prefers cup A to cup B or can't tell the difference between them;

Let us writeA ~ B (indifferent)if Ward can't tell the difference between cup A and cup B.

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.

Cup C was brewed using 15.5 teaspoons of coffee in the pot.

Determine which of the following relations holds true.

1) A weak preference B?

2) B weak preference C?

3) A weak preference C?

4) A ~ B?

5) B ~ C?

6) A ~ C?

Which of these collections of properties describes Ward's preference relations?

1)

Ward's "can't tell the difference" relation is transitive, Ward's "at least as good as" relation is transitive.

2)

Ward's "can't tell the difference" relation is NOT transitive, Ward's "at least as good as" relation is transitive.

3)

Ward's "can't tell the difference" relation is transitive, Ward's "at least as good as" relation is NOT transitive.

4)

Ward's "can't tell the difference" relation is NOT transitive, Ward's "at least as good as" relation is NOT transitive.