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To make preferences a little more mathematical, economists like to construct utility functions; when an individual gains more utility from one bundle of goods, he/she will prefer that bundle of goods to another bundle that provides a lower utility.

Assume that everyone has a very basic utility function for cake and ice cream: the more they eat, they more utility they get, and this relationship is linear; in other words:

$$\text{U(cake,ice~cream) = cake + ice~cream}$$

...where $\text{cake}$ and $\text{ice cream}$ is the slices of cake and scoops of ice cream one consumes, respectively (so they will prefer the bundle with more total cake and ice cream).

Which of the following preference relationships are true?


$(10,10) \sim (20,0)$


$(3,4) \succeq (5,6)$


$(5,5) \prec (6,6)$


$(5,0) \succ (0,5)$


$(1,9) \preceq (7,3)$


$(8,9) \sim (11,1)$

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