Question

So I have this FOL question with the following key:

A-forall

E-there exist

|-or

&-and

B(x):x is a basketballer

F(x):x is a footballer

S(x): x is a swimmer

H(x,y):x is more lazy than y

Now, we were asked to represent "Only basketballers and footballers are more lazy than every swimmer". I interpreted it as an Only A's are B's situation and according to what I know, you represent that by Ax(B(x)->A(x)).

So that is what I did. Ax( (B(x)|F(x)) -> Ay(S(y) -> H(x,y)) ). The system said it is wrong. I switched it around to 'if you are an swimmer and there exists someone more lazy than you, then that person is either a footballer or a basketballer'. Still wrong

It has been downhill form there. I have checked every other way I can think about this. Nothing is working. I thought the every was the issue but I have checked like three textbooks and none of them that have a part on symbolizing "every" has done anything other than a forall.

Is there something I am missing?

Answer 1

In FOL, 'every' is usually translated as a universal quantifier (∀), but difficulties might arise from the structure or usage of variables and quantifiers, not just from the symbolization itself. Checking the logical expressions' structure and variable application is recommended.

Step-by-step explanation:

It seems you are grappling with the challenge of symbolizing the word 'every' within the context of formal logic, specifically in First Order Logic (FOL). When working with FOL, 'every' is generally translated as a universal quantifier, which is represented as ∀ (for all). However, it is crucial to understand that it is not just the symbolism that matters, but also how you apply it within a statement. For example, to express 'Every human is mortal', you would write ∀x (Human(x) → Mortal(x)), where x represents any member of the domain and the arrow (→) represents logical implication.

Issues with FOL expressions often arise frsom the structure of the logical statement itself or how variables and their quantifiers are being used. If you are still experiencing difficulty, consider revisiting the structure of your logical expressions and ensuring that each variable, quantifier, and predicate is applied correctly in the statement you are trying to formalize.