"Each person's car" vs. "each persons' car" [closed]

Which of the following is correct?

• Each person's car has four wheels.
• Each persons' car has four wheels.

"Each" refers to a singular. Hence, it should be:

Each person's car has four wheels.

First off, the correct answer is "each person's".

Why? each is a determiner of English representing universal quantification. This quantifier states that a predicate is true for everything or everything of a particular subset. Here, the set is all cars and the predicate is something like "x has four wheels". This can then be formalized to something like: ∀xP(x), x∈{cars} and P(x)=x has four wheels. The nature of this quantification means that x must be singular in number. If it helps, think of a foreach loop in various programming languages.

The 's is a different issue. Without delving too much into X-Bar theory, here's a simple explanation. The 's too is actually a determiner and is dominated by the first Determiner Phrase. For example, a simple model:

[DP each person [DP 's car]].

This matches other languages (like German) nicely where the genitive is still represented by a "full" word. This also lets you get away with wild things like: "[the man who lives over by the field and has red hair]'s car has four wheels."