Question

This question is adapted from our textbook. Richard is an oldfashioned
Englishman who likes his tea with milk and sugar. Though he prefers more
sugar to less, he cannot always distinguish between two cups unless the difference in
the amount of sugar is less than a third (< 1/3) or more than one (> 1) teaspoon. If
there are two cups of tea where the difference is between a third and one teaspoon of
sugar, he is indifferent between them.
(a) Is Richard’s strict preference relation complete and transitive? Explain or give a
counterexample.
(b) Is Richard’s indifference relation complete and transitive? Explain or give a counterexample.
(c) Is Richard’s weak preference relation complete and transitive? Explain or give a
counterexample.