Suppose that FOIL is considering adding a literal to a clause using a binary predicate P and those previous literals (including the head of the clause) contain five different variables.

a. How many functionally different literals can be generated? Two literals are functionally identical if they differ only in the names of the new variables that they contain.

b. Can you find a general formula for the number of different literals with a predicate of arity r when there are n variables previously used?

c. Why does FOIL not allow literals that contain no previously used variables?