Suppose a prolog database gives you information about states and capital cities. Some cities are big, others small. Some states are eastern, others are western.

a. Write a query to find all the small capital cities.

b. Write a query to find all the states with small capital cities.

c. Write a query to find all the eastern states with big capital cities.

d. Formulate a rule to define cosmopolitan cities as big capitals of western states.

e. Write a query to find all the cosmopolitan cities.