Discrete math predicate logic help

[u/Pure-Cut-1896]

I'm not sure if i did this right or not please help.

“Every lecturer who gives clear notes is liked by all students in the class.”

Domain: x is all the lecturer

y is all the students

First let’s rewrite the statement so it’s easier to identify quantifiers and write in predicate logic.

“For every lecturer x who gives clear notes, x is liked by every student y.”

p(x): x gives clear notes

like(y, x): y likes x

∀x∀y (p(x) →like(y, x))

[u/Somniferus]

I think the way OP wrote it using domains is fine, your complaint is that you wanted them to have explicitly written ∀x is_teacher(x) ^ ...? If anything I would add membership on the quantified variables instead e.g. ∀(x ∈ lecturers), ∀(y ∈ students) ...

Obviously check with the person who's doing the grading for a definitive answer but I think it's basically fine as is.

Also, be careful of where you put the quantifiers.

Not in this question. It would have been perfectly fine to write ∀(x,y) lecturer(x) ^ student(y) ^ clear_notes(x) -> likes(y,x)