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Should the verb phrases following either and or in an "either or" sentence have the same structure?

For example, is the following sentence correct?

The coordinates of the points are either given or can be easily calculated.

An alternative to that sentence might be :

The coordinates of the points can either be given or be easily calculated.

I want to use the first one and wonder if it is correct or not.

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    I wouldn't use it; the deletion implies 'The coordinates of the points are given or the coordinates of the points are can be easily calculated.' Moving 'either' before 'are' makes the parallel structure integritous, but doesn't sound too colloquial. 'Either the coordinates of the points are given, or they can be easily calculated.' works. – Edwin Ashworth Aug 15 '14 at 10:19
  • @EdwinAshworth : Thanks for the reply. The context of the sentence is like this: In Figure 1, there are some red points. {the sentence}. Do you think that the last sentence suggested by you fits this context well? – user1639413 Aug 15 '14 at 10:36
  • @EdwinAshworth : I found this sentence on a website of the UK: Anticoagulant medicines are either given by injection (eg, heparin) or can be taken as a tablet. – user1639413 Aug 15 '14 at 10:39
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    '... the coordinates of some points are given; those of the others can be easily calculated.' // Yes; I said 'I wouldn't use it'. Deletions tend to mangle accepted grammar; this isn't a bad one, as the meaning remains clear. But imagine it in bullet-point format: Anticoagulant medicines are either (a) given by injection (eg, heparin) // (b) can be taken as a tablet. (I can't format vertically here.) – Edwin Ashworth Aug 15 '14 at 10:48
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    The first one is clearly better than the second one. The second says that either the points can be given or else they can be easily calculated. It's grammatical, but it's not what you mean. To improve the first one, you should move the "either", as Edwin says. – Peter Shor Aug 15 '14 at 11:08
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Edwin Ashworth's comment explains the structural problem that exists in the first option: The point at which either appears creates a node from which (usually) two parallel ideas emerge. Structurally, the words preceding either in the sentence or clause apply equally to both parallel ideas. Thus the sentence

The coordinates of the points are either given or can be easily calculated.

contains two parallel ideas that logically consist of these words:

The coordinates of the points are given.

and

The coordinates of the points are can be easily calculated.

Obviously, the are in the second parallel construction shouldn't be there, and it's easy enough to get rid of. In fact, you have multiple options for avoiding the structural anomaly. For instance:

The coordinates of the points either are given or can be easily calculated.

Either the coordinates of the points are given or they can be easily calculated.

The coordinates of the points are given or can be easily calculated.

Alternatively, you can avoid the problem by dispensing with the either/or construction altogether. For example:

If the coordinates of the points are not given, they can be easily calculated.

If the coordinates of the points are missing, you can easily calculate them.

I should emphasize that I'm talking about the structural logic of your original sentence—not about its comprehensibility to people who are fluent in English and therefore able to look beyond the actual structure of the sentence to glean its intended meaning. In general, you're better off avoiding flaws in parallel structure than leaving to each of your readers the task of silently (and perhaps subconsciously) correcting them for you.

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Yes, the first sentence is acceptable (and better than the second).

If they were separate statements, one would have:

  • ... the points are given
  • ... the points can be easily calculated (or calculated easily...)

To combine them, you wrap the 'either' and 'or' around the verb (or verb-adverb combination).

... the points are either given or can be calculated easily.

Extend with commas when you have multiple clauses, with the comma/or following the verb/adverb combos:

... the points are either given, can be calculated easily or looked-up in the reference table.

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