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Consider a preference relation on a finite set X={x1,x2,…,xn}. Suppose that it is complete and transitive. Then, the following function represents it: U(xi)= 3log|{j=1,…,n: xi at least as good as xj}|-2020, where |.| represents the cardinality of a set.

A marketing firm is interested in learning about millennials’ preferences on learning experiences. In order to do this, they survey students at a university. They ask them six questions as follows. They consider the following leaning experiences: a traditional class, a flipped course (half of the content is delivered online), and an online class. For each pair of these alternatives, say a and b, they ask the students “is a at least as good as b.” In order to make this operational, they provide the students with a picture in which the three alternatives are depicted as circles with their description next to it. The students are asked to draw arrows between the alternatives whenever the answer to a question is affirmative. That is, if a student finds alternative a is at least as good as alternative b, the student is asked to draw an arrow from the circle with label a to the circle with label b. (No question is a at least as good as a was asked; assume that the answer to each of these trivial questions is affirmative.) Suppose that a student’s answer has no arrows.

Julia has preferences on bundles of two commodities. The following figure shows one of her indifference curves. This curve is actually a line that passes through bundles C and D. Suppose that all other indifference curves of Julia are lines with the same slope as the indifference curve shown. What is Julia’s preferred bundle from all the bundles in the segment of line that joins bundles A and B?

Maria has preferences on bundles of two commodities with the indifference map shown in the following figure.Maria prefers to have bundles with larger amounts of the commodities. That is, adding an amount of a commodity to one bundle makes Maria better off. What is Maria’s best bundle from A, B, C, D, E?

Ana has preferences that are encoded by the Utility function U(x,y)=ax+y where a is a positive number. What is the value of a if Ana is indifferent between bundles A and B shown in the picture?

Recall that we say an agent prefers alternative a to alternative b if a is at least as good as b, but b is not at least as good as a. Jane prefers a to b, b to c, and c to a.  Based on this information, what properties are violated by Jane’s preferences (only one answer is correct)?

Let A = {1, 2, 3, 4} and B = {3, 4, 5, 6} be two events in a sample space S = {1, 2, 3, 4, 5, 6}. Select all elements in .

Unlike the Pyramids of Giza, the structure shown above is a ___________ whose original design emerged in the ____________

 When a soul enters the underworld, it is first met by _________the god of ____________

The object shown in the image above originated in the ______________ region of Mesopotamia, that rose to power after the Sumerians.