Professor Uptite likes students in his class to be highly participating, fast thinker and very solution oriented. If student A is better than student B in two of these three characteristics, then the professor prefers A to B, but if B is better than A in two of these three characteristics then Uptite prefers B to A. Otherwise, Uptite is indifferent between them. Cherelle, one of the students, is very participant, but slow thinker and is fairly solution oriented. Shivana, is fairly participant during classes, thinks very fast and is very solution oriented. Leela barely participates during lectures, thinks at average speed and is extremely solution oriented.
a. Does Uptite prefer Cherelle to Shivana or vice versa? Does Uptite prefer Shivana to Leela or vice versa? Does Uptite prefer Cherelle to Leela or vice versa?
b. Do the professor’s preferences satisfy completeness, reflexiveness and transitivity? Why or why not? Briefly explain.
c. Suppose, after some therapy sessions, professor Uptite decides to change his way of judging students. According to his new preferences, Uptite prefers student A to student B, only if A is better than B in all three of the characteristics and prefers B to A if B is better than A in all three characteristics. He is indifferent between A and B only if they are equally competent in at least 2 out of 3 categories. Are professor Uptite's new preferences complete? Are the professor's new preferences transitive? Are his new preferences reflexive?