# Help with Converting Sentences to FOL

• MHB
• hanzla

#### 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.

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

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

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))

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.

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?

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

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

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

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