Plural object possessive

Question

Which is correct if all the chairs have the same cover?
"The chairs' covers," or "The chairs' cover."

Answer 1

The crux of this question is distributive plural vs distributive singular. According to Quirk (he's not infallible, but I'll stick with him for this q), both the chair's covers and the chair's cover are correct, although covers is preferred.

While the distributive plural is the norm, the distributive singular may also be used to focus on individual instances. We therefore often have a number choice:

• The students raised their hand(s).
• Some children have {understanding fathers / an understandg father}.
• We all have {a good appettte / good appetites}.

The singular is sometimes obligatory or preferable with idioms and metaphors:

• We are keeping an open mind. [?open minds]
• They vented their spleen on him. [*their spleens]
• They can't put their finger on what's wrong. [*their fingers]

The distributive singular is sometimes used to avoid ambiguity:

• Students were asked to name their favourite sport.

The singular makes it clear that only one sport was to be named. Similarly:

• Children must be accompanied by a parent.

In The Oxford Dictionary of English Grammar, Sylvia Chalker writes:

Distributive plural concord is common in expressions such as The children all had such eager faces (where clearly each child had only one face), but a distributive singular is often possible, e.g. They all had such an eager expression.

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In the comments above it was debated whether both of these were correct:

A) The chairs' covers are all the same.
B) The chairs' cover is all the same.

Both sentences belong to standard English, but they differ in meaning. Their structure is:

A) [plural distributive subject] all [plural collective predicate].

B) [singular distributive subject] all [singular predicate].

A caveat is here in place that the plural predicate in A, as it turns out, is not distributive, but collective. A collective predicate is one that applies to a number of things jointly, rather than to each individually; examples are surrounded the house, are putting on a play, outnumber, and are arranged personwise. An example of a distributive one would be in Tom, Dick and Harry are eating lunch, which is identical to Tom is eating lunch, and Dick is eating lunch, and Harry is eating lunch. If Tom, Dick and Harry surround the house, they do it jointly;^{philosophy linguistic} dissimilarly, they eat individually. It's nonsensical to observe in isolation, This chair's cover is the same. The same with what?! _Hey guys, you'll never believe what I saw today. I saw this, this chair cover. It was the same! —Whaa? _ The predicate are the same, simply, cannot be de-distributed; thus, it never was distributive. Contrastingly, with a collective predicate, it is entailed that the predicate is never true of the individual things making up the group.^{linguistics philosophic}

OK, but what's the difference in meaning between a collective and a singular predicate? This is a good place to point out that in A all is a pronoun referring to covers—to this one, that one, that one over there, every one of them. However, in B all is an adverb and means "wholly; completely."

Therefore, A juxtaposes all particular covers and says they look identical, whereas B singles out one "generic" cover, juxtaposes all of its parts and says all smaller sections of the fabric look identical. That's a huge semantic difference!

Maybe plugging in different words, but keeping the structure, could prove helpful:

A) Their lives have all been the same.
B) Their life has been all the same.

The former deals with entire lives and says they have proceeded in likewise fashion (perhaps they all went to college, got married afterwards, had kids, dedicated themselves to their careers and received a Nobel Prize). The latter deals with parts of life, and even though they all have a life, referred to distributively by one "generic" life, their lives might be very much different (somebody's might be, say, an accountant, and somebody else might be a librarian), except for being unchanging (e.g., boring day in day out, or exciting day in day out).

So, no, A and B are not both "correct." Only A is "correct."

Answer 2

The chairs' cover.

"The chairs' covers" implies there are multiple covers. "The chairs' cover" implies all the chairs are covered by the same thing.

If you mean that the chairs all have their own covers but are the same kind of cover then you would use "the chairs' covers."