Determine if the following statement true or false: "A null set is a subset of any

given set S." and provide a proof.

Prove the following statement valid: "When 2 sets are equal, they must be subsets

to each other.".

Consider a function with 3 variables, say a utility function = (, ), where x

and y are two commodities that contribute to the level of the utility, u, through the utility

function, U. Construct a 3-D diagram to show the general shape the given function.

When answering this question, one should make sure the following: 1) explain how the

diagram is constructed; 2) the diagram should be theoretically correct by microeconomics

theory; 3) the diagram should be completely labeled.

Suppose Jan lives in a town where people drink coffee or/and tea, only. Coffee

and tea are considered substitutable for consumers. When people drink coffee or/and tea, they always take milk. Milk is complementary to both coffee and tea consumption. Construct a

mathematical model to show the local drink market and its general equilibrium.

Note: Construct and explain the model in a general way only, without actually solving it. If

you decide to make the model numerical, make sure the ingredients of the model are

consistent with microeconomics theory