MHB Help with Converting Sentences to FOL

[hanzla]

Hi, I need to convert below senteces into FOL, but I have difficulty doing it. Could someone peale help?

Lara ate exactly two apples.

Every city is either smaller than London or polluted.

 

[Evgeny.Makarov]

Start by determining the relations used in these statements and giving names to those relations.

 

[solakis1]

Hi, I need to convert below senteces into FOL, but I have difficulty doing it. Could someone peale help?

Lara ate exactly two apples.

Every city is either smaller than London or polluted.

The 2nd sentence can be converted in a way more accessible to pridicate calculus so we have :

if x is a city then x is smaller than London or x is polluted

Your pridicates here are: is a city , is smaller than, is polluted 1st and 3rd are one pridicates and the 2nd a two place pridicate:

Now denote:
is a city by capital C
is polluted by P
Is smaller than by S
London by L

Can you carry on from here

 

[hanzla]

We symbolize like this C(x): x is a city
P(x): x ia polluted
S(x): x is smaller than y
l for London

Does it have sa quatifier, cose its true for very city? Does the symbolization look like this?
∀x C(x) → (S(x,l) V P(x))

 

[Evgeny.Makarov]

S(x): x is smaller than y

You forgot the argument y of S.

∀x C(x) → (S(x,l) V P(x))

Correct, but it is better to enclose everything after ∀x in parentheses.

 

[hanzla]

I also have doubt about sentence `London is not a polluted city.` Is it correct like this. C(x): x is a city; P(x): x is polluted; l for London
¬P(l) ∧ C(x) does it need a identifying quantifier too?

 

[Evgeny.Makarov]

The formula is $C(l)\land\neg P(l)$. I am not sure what the phrase "identifying quantifier" means.

 

[hanzla]

Its existantial quantifier ∃ and it says “for some”, “there exists”, “there is a”, or “for at least one”.
∃x C(l)∧¬P(l)

 

[solakis1]

Its existantial quantifier ∃ and it says “for some”, “there exists”, “there is a”, or “for at least one”.
∃x C(l)∧¬P(l)

The above ∃x C(l)∧¬P(l) is not correct .The correct formula is

$\exists x(C(x)\wedge\neg P(x))$ or simply $C(l)\wedge\neg P(l)$

Only when you have a variable x,y,z...you can use a quantifier