For the question below, use these symbols correspondingly:

Preference relation: ?

Strictly preferred to: ?

Indifference: ~

Is a subset of: ? i.e. A ? B means A is a subset of B

Please bold things like R (real numbers), R+ means positive real numbers, vice versa.

3. [Upper/lower contour sets and indifference curves are an important part of our toolkit for reasoning about preferences. This example gives you some practice deriving them from preferences. Let X = R2, and let a denote the vector (3, 3) E X. In each part of this question, we will name a preference relation (you should convince yourself the relations we name are in fact preference relations, but you don't need to prove it), and ask you to draw a picture of various sets associated with it. (a) Consider the preference relation YES defined on the previous problem set. What does the "weakly better than" set ByEs (a) look like? What does the "weakly worse than" set WYES () look like? (b) Consider the preference relation ~1 given by a