Either my parents or my sisters IS/ARE going to visit...
Either my parents or my sister IS/ARE going to visit...
Which one is "certainly" correct?
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Either my parents or my sisters are going to visit.
Either my parents or my sister is going to visit.
The way I learned it (as native speaker) is that, when the subject is "A or B", the verb agrees with the noun closest to the verb (i.e., B).
Bear in mind that you will still be understood by native English speakers even if you used "are" instead of "is," even in writing. I don't care, at least. :) Nevertheless, if you want to be really correct, just use "parents" last so you always use "are" regardless of the number of sisters in the subject.
Either my sister or my parents are going to visit.
Either my sisters or my parents are going to visit.
Here's the breakdown on how people think the phrase is constructed:
The wrong way: Either/Or construction: The sentence is a compound of two independent clauses
[conjunction]"either" [noun phrase]"my parents" [conjunction]"or" [noun phrase]"my sister(s)" [verb phrase]"are going to visit"
Can be reconstructed as:
It's mistakenly thought that the sentence has two noun phrases and two verb phrases being combined into a single sentence:
See how this breaks down when sisters becomes singlar.
Now how do you combine the phrase? Thus your confusion.
Noun Phrase Construction
[adjective]"either" [noun phrase]"my parents or my sister(s)" [verb phrase]"are going to visit"
Should be read like so:
In english, a conjunction (the or part of the phrases in both construtions) can have a different grammatical case than its nouns (as it can have a different grammatical number than it's nouns).
So, the first construction, while seeming to make sense, is not honest in this case. It only makes sense to use are, since you're talking about two sets of things in both cases. Both of those individual cases could be single grammatically (either my parent or my sister are going to visit), and the conjunction can still use 'are' in relation to the verb phrase.
Just add a few more singular objects to see how natural it is to use are in regular spoken English:
How clunky would that sound to a normal, native English speaker to use is?
See: http://pinker.wjh.harvard.edu/articles/media/1994_01_24_thenewrepublic.html - the paragraph outlining the use of "Jennifer is / Jennifer are"