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I think in the following sentence it is correct to use "there exists":

There exists a number and two distinct elements [...]

But then, is the following sentence correct and if it is, why?

There exist two distinct elements and a number [...]

But if the second sentence is correct, should the first not use "There exist" as well as, via the "and", we refer to multiple things (a number AND two elements)?

2 Answers 2

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As to your question, both of them are correct.

There [singular verb] [singular subject] and [subject]

There [plural verb] [plural subject] and [subject]

There are apples and a banana. (correct sentence) 

There is a banana and apples. (correct sentence)

There is apples and a banana. (incorrect sentence)

There are a banana and apples. (incorrect sentence)

Also "and" makes both subjects plural as a whole as,

[Subject] and [Subject] + [plural verb]

Both you and I are nice.

They and I are beautiful.

Both they and I are beautiful.

Fruits and vegetables improve our health.

(but has some exception)

Slow and steady wins the race. (correct sentence)

  1. Slow and steady win the race. (incorrect sentence)

but you can write

  1. Both slow and steady win the race.
  2. Slow and steady people win the race. (correct sentence)

Because sentences 2 and 3 tell us about (some slow subject) and (some steady subject), which are two different subjects. But in sentence 1, there is one subject who is both slow and steady at the same time.

To write two different subjects and to use a plural verb with them, we can use "both" at the beginning of the sentence, like in (sentence 1), where an exception arises.

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  • So, what is the semantical difference between "There exists a number and two distinct elements" and "There exist a number and two distinct elements" - are there any conditions when one should be used, but not the other (or at least one is to be prefered)?
    – StefanH
    Commented Oct 25, 2022 at 13:00
  • 1
    There are no conditions to it. You could use either of it. In the practical world, psychologically(But I haven't any proves neither there are survey or tests on it), you could use "There exists a number and two distinct elements" to make it look singular. (even though it's not). "There are books and a pen" looks plural at first glance but "There is a pen and books" looks more like singular. But both sentences are plural. So you could use it however you want.
    – Rabi
    Commented Oct 25, 2022 at 14:24
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You are talking about several things, even though the first-mentioned happens to be one of its kind - so it's correct to use there exist.

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  • So, what is the semantical difference between "There exists a number and two distinct elements" and "There exist a number and two distinct elements" - are there any conditions when one should be used, but not the other (or at least one is to be prefered)?
    – StefanH
    Commented Oct 25, 2022 at 13:01
  • 2
    I'm not sure what sort of elements you are talking about, but I would say There are a vase and some books on the shelf - There are refers to all the things on the shelf, not just the vase. Commented Oct 25, 2022 at 13:09

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