What does it mean to say a consumer's preference relation is "convex" (resp., "strictly convex", "strictly monotone")? Define each of these 3 precisely. (b) Say the consumer has preferences that are continuous complete preorders (i.e., satisfy properties (1)-(4) per reflexive, complete, transitive, and continuous in my lecture notes/lectures). Define the set of "indifferences curves" for this consumer at for an arbitrary consumption bundle. Can "indifference curves" in this case be "thick" (i.e., sets with interior points, not "thin curves" as we usually draw them. (c) in part (b), now show if preferences are continuous strictly monotone complete preorders (i.e., satisfy assumptions (1)-(5) in my lecture notes, indifference curves cannot intersect. Further, show that indiffer- ences curves cannot be "thick" like in part (b). (d) Say preferences only satisfy assumptions (1)-(4) and (6) (convexity) in my notes. That is, they are continu- ous complete preorders that are additionally "convex". Can indifference curves cross?