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Well, I have done some sentences with the word "none" and written some interpretations according to the phrases. Please examine them for me,thanks.

None of the people in this city is alive.
Interpretation : No one is still alive in the city, I meant(can it be mean?) all of the remaining are virtually(can it be in fact?) zombies.

None of the people in this city are alive.
Interpretation : Same meaning as the above phrase but just want to make sure "is" and "are" are able to be used in this condition.

None of your apple has been eaten.
Interpretation : No part of your apple has been bitten by anyone else.

None of your apples has been eaten.
Interpretation : All your apples are remaining intact.

None of your apples have been eaten.
Interpretation : Same as the above one, but just want to know whether "has" and "have" are also able to be used in this situation or not.

Million thanks!
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From a strictly grammatical point of view all your examples are correct. However, English is a language of fixed phrases and expressions and the slightest deviation from what most people prefer to say may sound unnatural to some. Just a day or two ago, there was a thread containing this sentence: All I need is cigarettes. Somebody posted a reply saying all I need is a cigarette was the most natural version. That made me wonder how it could be the most natural choice even if this "I" needed more than one cigarette! English works in mysterious ways.

You'll have to wait for a native speaker's reply but I don't think people very often say none of your apple has been eaten even though it is perfectly grammatical. I may be wrong, of course! If they don't say that, I wonder what they say instead?

CB
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Hi, CB. I agonized over these for half an hour last night and decided it was just stressing me out. The esteemed usage panel in my American Heritage couldn't reach a two-thirds majority on the ambiguous ones, even with context.

And I agree with you that someone preparing for a journey may feel he needs more than one cigarette.
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According to Merriam Webster's Dictionary of (American) English Usage, "Clearly none has been both singular and plural since Old English and still is. If in context it seems like a singular to you, use a singular verb; if it seems like a plural, use a plural verb. When none is clearly intended to mean not one or not any, it is followed by a singular verb."
But how do you tell? If the sentence has a prepositional phrase "of the XXX" after "none" and the XXX is singular, the verb is singular. If XXX is plural, then the verb is plural. (Sometimes you will have to augment the sentence by adding a prepositional phrase )

Examples

Fifty percent of the pie has disappeared. Singular. Pie is the object of the preposition of.
Fifty percent of the pies have disappeared. Plural. Pies is the object of the preposition.
One-third of the city is unemployed. Singular.
One-third of the people are unemployed. Plural

All of the pie is gone. Singular.
All of the pies are gone.Plural
Some of the pie is missing. Singular.
Some of the pies are missing. Plural
None of the garbage was picked up. Singular.
None of the sentences were punctuated correctly. Plural
Of all her books, none have sold as well as the first one. Plural
So look at your sentences and follow the rules.
Note:
Of course, there are the special cases, as in Agatha Christie's novel entitled "And then there were none" (not one, not any), but then, this is British... Emotion: smile
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AlpheccaStars According to Merriam Webster's Dictionary of (American) English Usage, "Clearly none has been both singular and plural since Old English and still is. If in context it seems like a singular to you, use a singular verb; if it seems like a plural, use a plural verb. When none is clearly intended to mean not one or not any, it is followed by a singular verb." Of course, there are the special cases, as in Agatha Christie's novel entitled "And then there were none" (not one, not any), but then, this is British...

I think anyone versed in the basics of English grammar knows that none can be both singular and plural. It's just that some uses may appear unnatural to some. I take it that everybody is content with the original poster's sentences?

And then there were nonesounds good to my ear, be it British or American! Emotion: smile I assume that even Americans had more than one person in mind when Frank Sinatra directed a movie entitledNone But The Brave.

CB
American's of my generation (and Agatha's) were well indoctrinated in the notion of a plural "none," since Agatha's inspiration was an American nursery rhyme.