- #1

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Lara ate exactly two apples.

Every city is either smaller than London or polluted.

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- MHB
- Thread starter hanzla
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- #1

- 4

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Lara ate exactly two apples.

Every city is either smaller than London or polluted.

- #2

Gold Member

MHB

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

- #3

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

Lara ate exactly two apples.

Every city is either smaller than London or polluted.

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

- #4

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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))

- #5

Gold Member

MHB

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You forgot the argument y of S.S(x): x is smaller than y

Correct, but it is better to enclose everything after ∀x in parentheses.∀x C(x) → (S(x,l) V P(x))

- #6

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¬P(l) ∧ C(x) does it need a identifying quantifier too?

- #7

Gold Member

MHB

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

- #8

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∃x C(l)∧¬P(l)

- #9

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

∃x C(l)∧¬P(l)

$\exists x(C(x)\wedge\neg P(x))$ 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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