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I understand that it is an English rule that when 'each' or ' every' comes after a compound subject, a plural verb is used. What I cannot get my head around is that the sentence is still, in fact, talking about a singular subject.

Is this just one of the quirks and anomalies of the English language, or is the sentence logically talking about a singular subject?

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I think the fundamental meaning of the sentence is the same whether the "each" is placed after the subject or before. However, the number of the subject (singular/plural) is different.

Having this compound subject makes things confusing, as there are many ways of writing the sentence, depending on how verbose you want to be. For example:

  • Each student and [each] instructor hopes...
  • Each of the students and [each of] the instructors hopes...
  • The students and instructors each hope...

For the sake of making this simpler, I will go with the following examples:

  1. Each student hopes
  2. Each of the students hopes
  3. The students each hope

Sentences 1 and 2 take a singular verb, "hopes", because the subjects are singular. To determine the subject, we can ask "Who hopes?" The answer to this question for Sentences 1 and 2 is "Each student (S)" and "Each of the students (S)", respectively. However, in Sentence 3, the verb is plural, "hope", because the subject is plural. The answer to the question "Who hopes?" is "The students (P)". In this sentence, "each" is sorta just pointing back to the subject.

It helped me to see what's going by using subject pronouns:

  • Each of us hopes
  • We each hope

It's clearer from this that "We" is used as a plural subject, taking a plural verb. The "of us" is also not in a subject form, and the subject of this first sentence is singular: "Each (of us)".

I hope that helped and didn't confuse you more! This is a weird one.

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