I have written the phrase:

"The set of elements whose each pair is ...".  

Is the 'whose each' acceptable?

I was trying to ask this question in Quora, and the phrase I would like to write is "I would like to know sets of at least 3 words, whose each pair of words are false friends".

EDIT: (By FumbleFingers)

I was hoping for something like this answer to the same question on ELU. I can't fully endorse any recent answers here, so unless anything changes today, default bounty assignment will apply...

the highest voted answer created after the bounty started with a minimum score of 2 will be awarded half the bounty amount. If two or more eligible answers have the same score (i.e., their scores are tied), the oldest answer is awarded the bounty. If there's no answer meeting those criteria, the bounty is not awarded to anyone.

  • I think whose is more appropriate in case of person, not necessarily, but in most of the cases.
    – Mistu4u
    Commented Feb 13, 2013 at 3:07
  • 2
    I think we need a bit more of the sentence. It's not clear, at least to me, what is is you are really trying to convey here so I'm not sure if something like, "The set of element pairs such that each pair is ..." makes sense yet. I have a feeling you can get rid of the possessive altogether but until we have the whole sentence I can't be sure.
    – Jim
    Commented Feb 13, 2013 at 3:55
  • I was trying to ask this question in Quora: quora.com/Languages/Which-multiple-false-friends-are-there and the phrase I would like to write is " I would like to know sets of at least 3 words, whose each pair of words are false friends"
    – Alex Grilo
    Commented Feb 14, 2013 at 13:41
  • "The set whose each pair of elements...".
    – Jon Hanna
    Commented Feb 15, 2013 at 13:11
  • Please add your link to Quora to the question. Comments may be deleted at any time, and the question isn't really understandable without the context.
    – DCShannon
    Commented Apr 15, 2015 at 21:18

7 Answers 7


As indicated by answers to Can “whose” refer to an inanimate object? on ELU, some people wouldn't be happy with OP's use of it here. I'm not one of them, and given how awkward it would be to avoid the word in OP's construction, I'd just ignore those pedantic prescriptivist grammarians who say it's wrong.

Note specifically Peter Shor's answer on that ELU question, with several examples of Shakespeare using whose to indicate association with inanimate objects.

Here are many thousands of written instances of "equations whose solutions", which is perfectly normal English. By the same token, there's nothing wrong with OP's ...sets of elements whose pairs...

Having (I hope) dismissed criticism of whose, I'd say that most native speakers would use every rather than each in OP's particular sentence. I know I said in another answer that using every in this way is usually a bit stylised/dated. But here it's just "formal", which is appropriate in a "mathematical" context.

I can't exactly explain why "every" is better than "each" here, and I very much doubt it involves any "grammatical rule". But to support my contention that it is "better"...

whose each response (0 hits in Google Books)
whose every response (142 hits)

Also note that the corresponding figures for "whose each/every pair" are 3/116, and for ...solution they're 5/27, which may suggest that mathematicians are less attuned to such subtle distinctions.

There seems to be some disagreement over the distinction between "less common" and "ungrammatical" here, so I'd like to quote from New Scientist - 5 Aug 1989 - Page 55

Rather it elaborates a millionfold democracy whose each unit is a cell.

I've been reading New Scientist every week for decades, and I honestly can't recall ever seeing a grammatical error get through their admirable proofreading procedures. It's also reasonable to assume the authors of Encyclopedia of British Writers, 1800 to Present know their own language...

Golding is an author whose each successive work deals with a different subject in a different time...

EDIT: More recent comments have identified a semantic ambiguity in OP's example that I hadn't originally noticed. I assumed whose referred to "elements" (i.e. - each element within the set contains multiple words, each of which is a false friend to every other word in that element). But apparently whose references "the set", within which each single-word element is a false friend to every other element/word in the entire set.

This is purely an issue of semantics that goes beyond the issue being queried here (whether the usage whose each is "syntactically valid" in OP's example sentence).

  • 2
    errr, OP does not say sets of elements whose pairs. The question is about whose each, which you then prove is not in general use (i.e. the type of English ell is all about) except by mathematicians. What gives?
    – mcalex
    Commented Feb 13, 2013 at 18:11
  • 1
    I'm not focussing on replacing whose with some variation I'm giving alternatives for whose each because it's wrong. I didn't include 'whose' on it's own for the edited (ambiguous, not grammatical) reason, and I didn't think the stylised/dated nature of 'whose every' warranted a mention (though the mathematical context is a good point). I could add that but don't need to, now you have, but none of that changes whose each.
    – mcalex
    Commented Feb 13, 2013 at 18:34
  • 1
    @mcalex: What can I say? I don't agree with your bald unsupported statement that OP's whose each is "wrong" in any meaningful sense - it's just not a common form compared to whose every, or indeed whose each and every Commented Feb 13, 2013 at 18:37
  • 1
    I concur in everything except your preference for "every". We can't know without context; but it is easy to imagine that the author might have had reasons for preferring each pair of which to every pair of which, and that would carry over to the version with adjectival each. Commented Feb 14, 2013 at 0:47
  • 1
    Suppose it's about time I join ELL, and voting this answer up is reason enough to do so right now.
    – Jon Hanna
    Commented Feb 14, 2013 at 1:34

The short answer, I'm afraid, is 'no'. Whose each is not grammatically correct.

I assume the phrase is referring to a list of elements, for which each element in the list has a pair (element?), and you are interested in said pair elements that exhibit a certain characteristic?

The way I would word this would be:

The set of elements where each element's pair is ...

Slightly more verbose, but also fine is:

The set of elements for which each element's pair is ...

To alleviate any confusion, there is nothing grammatically incorrect about The set of elements whose pair is... There is an ambiguity however as to whether the elements have the pair or the set does, so you wouldn't use that particular wording in this instance.

  • 5
    mcalex, how about "The set of elements 'for which' each element's pair is ..."?
    – user114
    Commented Feb 13, 2013 at 2:44
  • Per my own answer, clearly I disagree with this "not grammatically correct" line. Commented Feb 13, 2013 at 17:46
  • 2
    The ambiguity is not in the perfectly standard "whose each", but in how it applies. Indeed, it seems they meant pairs of the elements, and so "The set whose each pair of elements..." is what they meant.
    – Jon Hanna
    Commented Feb 15, 2013 at 13:13
  • 2
    @Araucaria "the man whose each dog bit me" is perfectly grammatical, it just sounds strange because it's a strange thing to say. If given a circumstance where you had to distinguish between a set of men, of whom some of their dogs had bitten you, but where there was only one man for whom all of their dogs had bitten you severally, then it would indeed be the perfect phrasing. The strangeness of the expression comes not from its grammar, which is fine, but from the unlikelihood of its utility.
    – Jon Hanna
    Commented Apr 15, 2015 at 12:46
  • 1
    @FumbleFingers No, it doesn't. Look at the examples.One such set is "car (english), car (german), car (romanian)". This is a set of three words in which each pair is a false friend, because car (english) and car (german) are false friends, car (english) and car (romanian) are false friends, and car (german) and car (romanian) are false friends. You have a list of words, without subelements, and you're considering each pair of elements. The pairs are not elements. The words are elements, and you consider pairs of them.
    – DCShannon
    Commented Apr 16, 2015 at 19:01

The structure of Noun Phrases

Simple noun phrases usually have two sections, a Determinative and a Head. The Determinative function is typically carried out by special words called DETERMINERS. The Head function is usually carried out by a phrase headed by a noun. This type of phrase we see inside a noun phrase is called a NOMINAL.

In the phrase a big dog, we see the following structure:

enter image description here

Now, because the nominal is a proper phrase in its own right, it has its own internal structure. Like all phrases, it has its own Head. It also very often has a Modifier. When this Modifier comes before the head, we call it an Attributive Modifier. Attributive Modifiers are very often adjectives. In the phrase big dog, the Modifier is the adjective, big, and the Head is the noun, dog.

Now, notice that I said that Determinatives are "typically" determiners, and that Modifiers are "often" adjectives. This is because other types of words and phrases can carry out these jobs. For example in the noun phrase:

  • John's Madonna t-shirt

... the Determinative is the genitive noun phrase John's, not a determiner. Similarly, the Modifier in the nominal is the proper noun, Madonna, not an adjective.

Notice also that both determiners and adjectives can carry out other functions apart from Determinative, or Attributive Modifier:

  • That was the fastest I ran.
  • Indignant, she waltzed out of the room.

Each versus Every

One of the other answers here brings up a comparison with each and every. At first blush, this seems quite reasonable. Firstly, both each and every are determiners. They also have some similarities in terms of meaning. For example, we can say that they sometimes give us a meaning somewhat similar to all:

  • All the men have finished their food.
  • Every man has finished their food.
  • Each man has finished their food.

The sentences above basically give us the same kind of information. There are no men who haven't finished their food. Notice from the sentence above that each and every have some similar grammatical properties too. For instance, they both take singular nouns: in the examples above we see "all the men", but "every man" and "each man". This is because every and each have DISTRIBUTIVE meanings. We consider that the verb phrase finished their food applies to each member of that group of men considered individually.

Another difference you might have noticed is that in the first example, all occurrs with the determiner the. The word all differs from prototypical determiners because it can occur with a different function in a special slot before the Determinative. Writers like Quirk et al (1985), call words like all "pre-determiners".

Determiners like each and every, the, a, this, no and also genitive noun phrases such as his, ones and Ben's have an important property: we can only have one of these types of words in Determinative function. The following phrases where we find two such words in Determinative function are therefore badly formed:

  • *The my dog is wagging its tail.
  • *A my friend is coming.
  • *The every man finished their meal.
  • *Each the book was shelved properly.
  • *No Ben's friend came to the party.

So we've seen that each and every have some similar properties: they're both determiners; semantically they have distributive meanings similar to all; they cannot occur in determinative function together with other central determiners or with genitive noun phrases.

However, at this point all similarity ends. Each and every have other semantic and syntactic properties which make them very different. We shall see that just because we can use every in a particular way, it does not mean we can therefore use each in that same way - or vice verse.

First of all, we can use each to stand in for an each + [noun] combination. We can't do this with every:

  • Give me one of each.
  • *Give me one of every. (ungrammatical)

Because of this we can use each on its own as an Adjunct after the Subject in sentences such as:

  • The baboons each gave the elephant a donut.
  • *The baboons every gave the elephant a donut.

We can also therefore use each and not every on their own in partitive expressions:

  • Each of them ...
  • *Every of them ...

A second difference that's important in terms of syntax is that we can freely modify the word every, but not the word each:

  • *Almost each dog ate a bone.
  • Almost every dog ate a bone.

In the first example we see each modified by the word almost with bad results. The example with every is fine.

There are many, many more differences between each and every, but, for the moment, I'll mention just one more: we can use every without a distributive meaning, mostly with abstract nouns. When we use it like this, it has a "multal" meaning. In other words it means something like "a lot of":

  • We gave him encouragement.
  • We gave him every encouragement.
  • *We gave him each encouragement.

We can see the non-count use of encouragement in the first example above. In the second example we see the same non-count use of the word encouragement. This example does not mean that there was a group of encouragements and we gave him all of them. It means we gave him a lot of encouragement or a variety of encouragement. The last example cannot mean the same thing. Encouragement here cannot be that non-count sense of encouragement. The determiner each cannot have a multal instead of distributive meaning.

The Original Poster's question

*The set of elements whose each pair is ... (ungrammatical)

The sentence above is ungrammatical. The reason is, simply, that whose is a genitive noun phrase, just like his or Ben's. We have already shown further above that each and every cannot be used together with genitive pronouns in Determinative function. I fact whose, like other genitive noun phrases, cannot be used with central determiners as Determinatives at all:

  • *A man whose the dogs bit him went to the hospital yesterday.
  • *The dictionary whose a page you tore out is missing.
  • *The elephants whose their donuts you ate has escaped.
  • *That man whose every toe was amputated went to the police.
  • *The wife whose each husband died in mysterious circumstances absconded.

The sentences above are all badly formed. They each try to use whose with another genitive noun phrase or determiner as a Determinative.

Some of the other comments here have noted that we can use whose with every in phrases like:

  • whose every move (grammatical)

We can also use every after other genitives such as his or her:

These posters argue that if whose every move is grammatical, then whose each move must also be grammatical. This does not follow though, because as we have shown, each and every do not have the same grammar. However, in any case this really isn't the key issue here anyway. The Original Poster's example is clearly asking about using whose each as a Determinative. We have shown that this is not possible.

The phrase whose every move does NOT use every as a Determinative, it uses it as a Modifier in the nominal every move. The word each cannot appear alone in this function. The structure for the phrase whose every move is:

enter image description here

As the Cambridge Grammar of the English Language (Huddleston & Pullum, 2002) states in its section on every versus each:

(g). Every, but not each, can occur as a modifier following a genitive [...].

[25] a. They scrutinised [her every move]. b. * They scrutinised [her each move].

The [ * ] next to example (b) there indicates that it is ungrammatical. Example (a) is structured [her] [every move]. It is similar in meaning to "[every move] of hers".

This clearly shows that we cannot use each as a modifier after genitives such as her or whose. (We can however use the idiomatic phrase each and every, which patterns the same as every here).


  1. I'm assuming that readers know that we can use relative whose to refer to both people and object. I won't address this here, Fumblefingers has links to relevant posts on that subject in his answer, if you'd like to read about it.

  2. I use the term Determiner in this piece, like the majority of modern grammars, to refer to the class of words. I use Determinative to refer to the function. Huddleston and Pullum reverse the established terminology in CGEL.

  3. John Hanna and Fumblefingers state in comments or posts that for them whose each is grammatical. It might be the case that whose each is grammatical in the OP's intended usage for speakers of some varieties of English. I'm most familiar with so-called Standard GB, and it might be that whose each is grammatical for some other groups of speakers.

  4. Man_From_India has suggested that phrases such as supported his each step and similar which might be grammatical. I don't think this is so. It is possible to find a few examples from Googlebooks (40 at first glance). However, these turn out mostly to be running across sentences ["his. Each step ..."], or else they are self-published unedited texts full of typos.Here's the Ngrams graph for his each step and his every step. As you'll see there are no results at all for his each step:

  • 2
    I assume no-one's going to argue that at the time John Dryden's We two have kept its homage in suspence, And bent the globe, on whose each side we trod, Till it was dented inwards. was "grammatical". I don't buy your reasoning as to why this is no longer the case, and although in general I'd use every rather than each in such contexts, I certainly wouldn't change that one. But I do agree with most of what you say, and maybe the rest is just opinion. Commented Apr 20, 2015 at 12:22
  • 2
    ...Obviously no-one is going to say Dryden's suspence is a valid spelling today, so we have to accept that some things change over time. Perhaps I've just spent too much time reading the classics, but whereas I don't mind labeling whose each "dated, poetic", I'm not comfortable with having it called "ungrammatical". Commented Apr 20, 2015 at 12:27
  • 2
    @Araucaria Is his a genitive? I think it is, because a possession is being meant using his. It's not uncommon to have his each, e.g - Then Salome knelt on her naked fours for to blow a gentle wind of breath into his each ears, Hospital staff carefully supported his each step. Then how each can't follow a genitive? I think I am missing something, can you please help? Commented Apr 20, 2015 at 13:30
  • 1
    @DamkerngT. Nice quote:) Things have changed though! As you will see from this page of the OED "The co-occurrence rules for determiners were somewhat different from those in later modern English. Notably common was the sequence of demonstrative + possessive + noun (‘this your son’)." This is exactly the type of example we're talking about. So it looks as though about five hundred years ago, that was indeed grammatical, but it isn't any more! Commented Apr 23, 2015 at 10:41
  • 1
    But, but, but what about: "Is this your son?" . . . Okay, okay, maybe there be a bit of subject-aux inversion in there, maybe. :D
    – F.E.
    Commented Apr 23, 2015 at 19:17

Set Up

The sets being referred to are described on Quora as such:

Formally speaking, I would like to know sets of at least 3 words, such that each two of those three words are false friends.

So the pairs are pairs of words that are false friends, within a larger set of words.

Suggested Phrasing

As I understand it, you're trying to refer to one of these sets. And you've tried to do it like so:

The set of elements whose each pair is ...

I would understand your meaning, but would pause at the awkwardness of the sentence. There may be some justification for this phrasing being technically grammatical, but it certainly doesn't sound right. If you put this in a paper, I would suggest you revise it.

Alternative Phrasing

I have a degree in mathematics, and have written more proofs involving sets than I would care to recall. To refer to one of these sets, you would say:

A set in which each pair of words are false friends.

So the phrase you're looking for is 'in which each pair'. You're describing 'which' set based on the set's elements, so talk about the elements. Elements of a set are 'in' the set, and a set is a thing, so it is better to say 'in which', not 'whose'.

Furthermore, the set doesn't directly contain pairs. The elements of the set are words, and then we create pairs to consider from these words. This reason also makes using the possessive 'whose' to indicate the pairs of the set seem less precise than referring directly to the elements with 'in which each'. In other words, the set doesn't have pairs.

We're stating a fact about each specific pair, that is a pair of false friends, not about the whole collection of pairs, so I would use 'each', not 'every'. One could use 'every', and this may be a personal preference. Consider this article when deciding.

Honestly, though, I'm a little thrown off by "each pair of words are false friends". It feels a little like I should be using 'is' rather than 'are', as a 'pair' is one thing. It would be more correct, if pedantic, to say:

A set in which each pair of words is a pair of false friends.

Which I would streamline into:

A set in which any two words are false friends.

  • Whilst it's true that a set whose every {element, whatever} is more common than a set whose each this doesn't mean the latter is actually "wrong" (at only 3 hits to 57, it's not necessarily that significant anyway). The question isn't about What does it mean?, it's about whether a less-common way of expressing the concept is grammatically valid or not. Commented Apr 16, 2015 at 1:52
  • @FumbleFingers I didn't say it was 'wrong'. In fact I suggested to use 'each'. He said he wrote a phrase, and wanted to know if was the right way to express the thought. I've explained how I would express it and why. Are you somehow reading this as not answering the question?
    – DCShannon
    Commented Apr 16, 2015 at 2:05
  • @FumbleFingers I made a significant edit. Maybe that's clearer to you?
    – DCShannon
    Commented Apr 16, 2015 at 2:28

OP quoted the following sentence and asked whether whose each construction is acceptable or not.

The set of elements whose each pair is ...

Reading briefly other answers/comments it's apparent that this is a debatable issue. But I don't see the reason. This is a correct construction.

Let's consider the following sentence -

The police said the accident that happened last night was unavoidable.

Here the relative clause is - that happened last night. The antecedent is - the accident. that refers back to the accident, and is the subject of the relative clause. The accident happened last night.

(I will restrict this discussion of the relative clause to this extent. As till this much is relevant here.)

He is the man whose dog poops at our garden every morning.

Here the relative clause is - whose dog poops at our garden. Antecedent is - the man. whose is the subject of the relative clause, and is the possessive of the man. The man's dog poops at our garden every morning.

whose is the possessive form of what or which, and can be replaced by of which. It can both refer to an animate as well as an inanimate object.

There is a myth about whose; I don't know if that still exists. As per the myth, only animate object (especially person, but animal is okay but frowned on) can be referred by whose. And it's objectionable for whose to refer an inanimate object.

As I clearly said the above style guide is just a myth, and this explains all.

This is a matrix whose each element is zero.

So here we can use whose each without any problem. Each element of the matrix (Matrix's each element) is zero.

  • @FumbleFingers I will change that :-) I am doing weird stuff today :-) for reason unknown. And in your answer you have cited some good examples. Commented Apr 16, 2015 at 14:31
  • They might be "good examples", but judging by current vote totals they haven't convinced everyone that OP's usage is valid. Hopefully your answer addresses the problem by showing why it's okay, rather than simply citing other writers who've used the format. Commented Apr 16, 2015 at 14:36
  • @FumbleFingers I am not very sure how convincing my answer is. I just tried to include how much grammar I know about this. I am waiting for Araucaria's answer. Commented Apr 16, 2015 at 14:39
  • 1
    The problem I have with this is not each/every or whose on an inanimate object. It's 'each' immediately after 'whose'. "Whose each" sounds insane. "Whose every" maybe, "in which each" sure, but "whose each" just makes my ears bleed. It's just too much of a mismatch in terms of talking about a collection versus the individual elements. I don't think it's a hard and fast grammar rule, so I can't say it's ungrammatical, it just sounds wrong to someone who's heard hundreds of hours of conversations about sets.
    – DCShannon
    Commented Apr 16, 2015 at 18:51
  • I think it's probably the concept of possessing an 'each' that's bothering me. You could have every, as that's all of them all at once, but it seems odd to consider owning the idea of a specific element in the set for all elements in the set. "My every attempt" vs "My each attempt", "His every word" vs "His each word", "Their every thought" vs "Their each thought". You're really saying none of those sound off to you?
    – DCShannon
    Commented Apr 16, 2015 at 18:57

It is acceptable, but not sufficiently explicit to be unambiguous to all readers. Is it correct? Well, in my opinion, the more important question is whether it is clear and unambiguous.

The problem, as was pointed out by one answerer, is that a set of three or more words does not, per se, "have" pairs. Thus, a possessive (whether whose or some other possessive), with or without each, does not adequately describe the process of selecting various pairs of words from the words which compose the set.

So the idea of possession is necessary but not sufficient to defining the pairs.

Yes, this is a question of semantics (or, if you will, of logic or mathematics).

If I had to suggest a better wording..... ah, but the OP did not ask for one.

  • I think you need to be careful about conflating attributes like unambiguous, correct, grammatical, here. Most likely, in context, to a reader who already knows and is interested in whatever the writer is talking about, there's no ambiguity whatsoever. So it's probably not even a valid criticism that "non-interested" people outside the target audience might be unsure about the referent of each. Cutting to the chase, +1 for It is acceptable. Commented Apr 20, 2015 at 14:32
  • Point taken. Removed my claim "It is correct if it is not ambiguous". Now I just say that in my opinion it is more important to ask whether it is clear and unambiguous. Commented Apr 22, 2015 at 7:21

I would object first to the example's placement of the word "each", and the explanation for why I would do is quite simple. "Whose" is a possessive pronoun, and the sentence must clearly convey to whom or what the pronoun refers. Here is your example sentence:

The set of elements whose each pair is ...

Can we match the pronoun "whose" to an antecedent written with what we have here? Let's see. To what does "whose" refer?

  • the set?
  • the elements in the set?

No, none of these are good answers. We know what we're trying to say with our sentence, and what we're trying to say has "whose" referring to each individual element in the set. To convey this correctly, we need to alter the word order of the sentence slightly so that the pronoun's antecedent precedes the pronoun itself, like this:

The set of elements, each whose pair is...

Restructuring the sentence like this makes it almost grammatically correct, though I will elaborate in a moment on why it still fails to communicate what we actually mean. Remember, though, that pronouns in English generally need their antecedents to be used before the pronoun is used so that the pronoun may be properly understood by the audience.

The set of elements, each whose pair is...

Let's return to this for a moment. The word "each" itself is serving as a pronoun here, referring to iterative individuals of a plural noun. But what noun is it referencing? It's "set", right? But "set" isn't plural--so how can we iterate through the individuals which belong to it? Indeed, we now face a problem that forces us to rephrase!

The set of elements, each of which whose pair is...

This phrasing is correct, but my, is it garish. It is ugly! Hideous! And, worst of all, it is convoluted! Somebody who isn't very familiar with the English language would probably become very confused very quickly by all the prepositions and pronouns. You could vastly simplify things breaking this whole expression up into more manageable sentences, like this:

The set is composed of many elements. Elements in the set which have a pair whose [...] is [...]...

This is about as far as the example sentence in the question can carry me. As you can tell, things get pretty complicated the more specifically you try to compose your statement. I'm afraid I can't explain any further without a full example statement to revise.

As for the matter of whether it is permissible to use "whose" in reference to an inanimate object, I believe @FumbleFingers gives a fantastic answer. I won't touch on that aspect of the question. There are many examples of using "whose" in this way.

  • I am sorry I beg to differ. I haven't read your full answer, but I have read till a few lines after your third quoted sentence. And I found whatever written within that span is completely wrong. Commented Apr 16, 2015 at 14:03
  • 1
    @Man_From_India The function of "each" in this context is complicated and not very approachable to a speaker whose first language is not English. The word "each", it can probably be agreed, does in fact refer all individual units within a collection. But this way of looking at things is nuanced in that correctly using the word "each" requires us to identify the individual units to which "each" refers. In the phrase which precedes use of the word "each", "of elements" is a preposition, and a close reading would interpret "each" to refer to the collection "set"--which is of course not plural.
    – R Mac
    Commented Apr 16, 2015 at 14:40
  • 1
    As I said I haven't read fully, my main problem is with your second and third quotation where you said each whose is almost grammatically correct, and mentioned that it doesn't communicate the meaning well. I think each whose is incorrect. Another problem is where you tested if whose each refers to its antecedent correctly. Commented Apr 16, 2015 at 14:58
  • To address your concern regarding "each whose", you might be right that I could edit my answer to clarify what I mean. What I mean is simply that "each whose" is a valid construction, but that construction does not mean what it is intended to mean in the given context. As for testing the antecedent of "whose each", the problem with the expression "whose each" is that "whose" is a possessive pronoun. Because it's possessive, when one says "whose each", "each" should be interpreted as the thing which is owned by the person or thing to which "whose" refers.
    – R Mac
    Commented Apr 16, 2015 at 15:20
  • Yes you are right. But your answer does say it's not clear which is the antecedent. Am I right? It's the noun phrase a set of elements. Commented Apr 16, 2015 at 15:28

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