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Say, an element 'a' occurs in two sets: X={'a','b'} and Y= {'a','c'}.

So, what preposition should be used in the blank of the following sentence:

'a' is common element ___ sets X and Y.

It's 'to', 'with' or 'between' ?

2 Answers 2

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You can use all three, but your sentence should read

'a' is a common element ___ sets X and Y.

'a' is a common element to sets X and Y.
'a' is a common element with sets X and Y.
'a' is a common element between sets X and Y.

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  • How woild you explain the use of 'to'? Dec 9, 2016 at 7:12
  • " 'a' is common to (both) sets X and Y."
    – Peter
    Dec 9, 2016 at 8:18
  • I see. We can omit 'both' right? Dec 9, 2016 at 8:36
  • Yes, "both" may be omitted, but personally I would say " 'a' is common to both X and Y" since it's probably already known that X and Y are sets and belonging to "both" is what is emphasized.
    – Peter
    Dec 9, 2016 at 16:33
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You can use between in this sentence 'a' is common element ___ sets X and Y. Between is used when naming distinct, individual items so it shows clear meaning.

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    Please edit to include an explanation of why this is correct; answers without explanation do not teach the patterns of the language well. Dec 8, 2016 at 7:27

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