Suppose a Prolog database exists that gives 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.