Notes

T akes(x, c, s): student x takes course c in semester s;P asses(x, c, s): student x passes course c in semester s;Score(x, c, s): the score obtained by student x in course c in semester s;x > y: x is greater than y;F and G: specific French and Greek courses (one could also interpret these sentences as re- ferring to any such course, in which case one could use a predicate Subject(c,f) meaning that the subject of course c is field f ;Buys(x, y, z): x buys y from z (using a binary predicate with unspecified seller is OK but
less felicitous);Sells(x, y, z): x sells y to z;Shaves(x, y): person x shaves person yBorn(x, c): person x is born in country c;P arent(x, y): x is a parent of y;Citizen(x, c, r): x is a citizen of country c for reason r;Resident(x, c): x is a resident of country c;F ools(x, y, t): person x fools person y at time t;Student(x), Person(x), Man(x), Barber(x), Expensive(x), Agent(x), Insured(x), Smart(x), Politician(x): predicates satisfied by members of the corresponding categories.

Some students took French in spring 2001.∃x Student(x)∧Takes(x,F,Spring2001).
Every student who takes French passes it.∀x,s Student(x)∧Takes(x,F,s) ⇒ Passes(x,F,s).
Only one student took Greek in spring 2001.∃x Student(x)∧Takes(x,G,Spring2001)∧∀y y̸=x⇒¬Takes(y,G,Spring2001).
The best score in Greek is always higher than the best score in French. ∀s ∃x ∀y Score(x,G,s) > Score(y,F,s).
Every person who buys a policy is smart.∀x Person(x)∧(∃y,z Policy(y)∧Buys(x,y,z)) ⇒ Smart(x).
No person buys an expensive policy.∀x,y,z Person(x)∧Policy(y)∧Expensive(y) ⇒ ¬Buys(x,y,z).
There is an agent who sells policies only to people who are not insured.∃x Agent(x)∧∀y,z Policy(y)∧Sells(x,y,z) ⇒ (Person(z)∧¬Insured(z)).
There is a barber who shaves all men in town who do not shave themselves. ∃x Barber(x)∧∀y Man(y)∧¬Shaves(y,y) ⇒ Shaves(x,y).
A person born in the UK, each of whose parents is a UK citizen or a UK resident, is a UK citizen by birth.∀x Person(x)∧Born(x,UK)∧(∀y Parent(y,x) ⇒ ((∃r Citizen(y,UK,r))∨ Resident(y,UK))) ⇒ Citizen(x,UK,Birth).
A person born outside the UK, one of whose parents is a UK citizen by birth, is a UK citizen by descent.
∀x Person(x)∧¬Born(x,UK)∧(∃y Parent(y,x)∧Citizen(y,UK,Birth)) ⇒ Citizen(x,UK,Descent).
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.
∀x Politician(x) ⇒(∃y ∀t Person(y)∧Fools(x,y,t))∧ (∃t ∀y Person(y) ⇒ Fools(x,y,t)) ∧ ¬(∀t ∀y Person(y) ⇒ Fools(x,y,t))
l. All Greeks speak the same language.∀x,y,l Person(x)∧[∃r Citizen(x,Greece,r)]∧Person(y)∧[∃r Citizen(y,Greece,r)]
∧Speaks(x,l) ⇒ Speaks(y,l)

W(G,T).
¬W(G,E).
W(G,T)∨W(M,T).
∃s W(J,s).
∃x C(x,R)∧O(J,x).
∀s S(M,s,R) ⇒ W(M,s).
¬[∃s W(G,s)∧∃p S(p,s,R)].
∀s W(G,s) ⇒ ∃p,a S(p,s,a).
∃a ∀s W(J,s) ⇒ ∃p S(p,s,a).
∃d,a,s C(d,a)∧O(J,d)∧S(B,T,a).
∀a [∃s S(M,s,a)] ⇒ ∃d C(d,a)∧O(J,d).
∀a [∀s,p S(p,s,a) ⇒ S(B,s,a)] ⇒ ∃d C(d,a)∧O(J,d).