I have searched for answers/help, but I am not able to find specifics. I am on a "FOL for Dummies" level, I really have no clue what I'm doing. Edit: I understand most of the symbols (∀x, the backwards E meaning there exists), I just don't know how to tie them together conclusively. I understand (barely) truth tables. Very basic knowledge of the information.
Having trouble with first order translations.
Assume the universe is all human beings.
(a). Some citizens are unhappy in countries ruled by dictators.
(b). No college dean is greedy.
Attempt: For this, I have ∀x (x is a college dean -> ~(x is greedy)), but I don't think that is what I am looking for.
(c). All freshmen that drink regularly never make A's.
Attempt: x= Freshman, P(x)=drinking, z=Making A's. (∀xP(x)) -> ~Z
AND
Consider the following formulas:
(a). [(∀xPx) v (∀xRx)] -> ∀x(Px v Rx) and
(b). [∀x(Px v Rx)] -> [(∀xPx) v (∀xRx)]
Which one is true in any model? Give a model where the other one is false.