Passing French: All Students

[Johnny Leong]

Represent this sentence in first-order logic:
Every student who takes French passes it.

Represent the sentence "All Germans speak the same languages" in predicate calculus. Use Speaks(x, l), meaning that person x speaks language l.

What axiom is needed to infer the fact Female(Laura) given the facts Male(Jim) and Spouse(Jim, Laura)?

 

[AKG]

Represent this sentence in first-order logic:
Every student who takes French passes it.

Represent the sentence "All Germans speak the same languages" in predicate calculus. Use Speaks(x, l), meaning that person x speaks language l.

What axiom is needed to infer the fact Female(Laura) given the facts Male(Jim) and Spouse(Jim, Laura)?

Hopefully, you can figure out the actual syntax yourself (I can't) but it might be helpful to see the first sentence as:

For all students, s, (s takes French) --> (s passes French)

For the third one, the axiom would be that only a male and a female can be spouses. Maybe:

For all x, y, (Spouse(x,y)) --> (male(x) <--> female(y))

Maybe also

For all x, male(x) <--> ~female(x)
OR
For all x, male(x) <--> !female(x)
depending on what notation you're using.

 

[R0man]

1. ∀x (Student(x) ∧ Takes(x, French) → Passes(x, French))
2. ∀x (German(x) → ∀l (Speaks(x, l)))
3. Spouse(Jim, Laura) → Female(Laura)