How to choose the correct quantifier in this case?

Question

I'm trying to write the statement below into first order logic:

If somebody has a car, then they don't walk.

My question here is about the quantifier. Is it correct to represent If somebody with all x ?

all x (HasCar(x) -> -Walk(x)).

Answer 1

Your analysis is correct.

It is worded confusingly.

"somebody" should be interpreted as "an arbitrary person".

Because $x$ is "arbitrary" we can go from the particular instance to the general instance. There is a term for this: Universal Generalisation: generalising to the universal from the fact that you know that your arbitrary instance could have been any such instance.

https://proofwiki.org/wiki/Universal_Generalisation

Hence it is reworded:

Let a person $x$ be arbitrary. If $x$ has a car, then $x$ does not walk.

That is:

For all $x$ (in the domain of "people"), $x$ has a car implies it is not the case that $x$ walks.

And you have correctly interpreted it.