Represent the following sentences in first$-$order logic, using a consistent vocabulary

$($which you must define$)$:

a$.$ Some students took French in spring $2001.$

Section $8\mathrm{.}5.$ Summary $269$

b$.$ Every student who takes French passes it$.$

c$.$ Only one student took Greek in spring $2001.$

d$.$ The best score in Greek is always higher than the best score in French.

e$.$ Every person who buys a policy is smart.

f$.$ No person buys an expensive policy.

g$.$ There is an agent who sells policies only to people who are not insured.

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

i$.$ A person born in the UK$,$ each of whose parents is a UK citizen or a UK resident, is a

UK citizen by birth.

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

citizen by descent.

k$.$ 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