Represent the following sentences in first-order logic, using a consistent vocabulary (which you must define as well).

a. Define the vocabulary. For example, you might have:

(i) Buys(X,Y,Z) = Person X buys Item Y from Person Z

(ii) W > Score(X,Y,Z) = W is larger than score Person X gets in course Y during semester Z

(iii) Predicates: Person(X), Clever(Y), Politician(Z)

It may make more sense to do question a. last.

b. Every person who buys a policy is clever.

c. No person buys an expensive policy.

d. There is a barber who shaves all men in town who do not shave themselves.

e. A person born in the UK, each of whose parents is a UK citizen or a UK resident, is a UK citizen by birth.

f. A person born outside the UK, one of whose parents is a UK citizen by birth, is a UK citizen by descent.

g. Politicians can fool some of the people all of the time, and they can fool all of the people some of the time, but they can't fool all of the people all of the time.

h. Some students took Russian in spring 2001.

i. Only one student took German in spring 2001.

j. The best score in German is always higher than the best score in Russian.