Counting the numbers of quantifiers, how are there 4?

45 Views Asked by At

From the book "Gentle Introduction to Art of Mathematics":

How many quantifiers does this have and what kind?

"Everybody has some friend that thinks they know everything about a sport.”

The answer given is "four", but no explanation has been provided.

I think that "everybody" implies Universal and "some" is Existential:

$$\forall p \in P, \exists f \in F \text{ who thinks they know everything about a sport}$$ $$P = \text{Set of all people}, F = \text{Set of Friends}$$

Perhaps we can write "everything" in some way, and I guess we can write "a sport" as "some from all the sport sets".

1

There are 1 best solutions below

2
On BEST ANSWER

"Everybody has some friend that thinks they know everything about a sport.”

We have everybody, some friend, everything, and some sport:

$$∀a{\in}P\;∃b{\in}P\;∃s{\in}S\;∀t{\in}T\; \Big(Fab ∧ (Rts→Kbt)\Big).$$