.
Therefore, according to your principle, the following are properly rendered with the singular verb, "is":
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None of the US presidents is women. (in lieu of "None ... are women.")
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None of Alaska's earthquakes since 1964 is so strong as this one. (in lieu of "None ... are so strong...")
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None of my socks is lost in the dryer. (in lieu of "None ... are lost...")
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None of the stars in the sky is brighter than the moon.
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None of the cans on the shelf is dented.
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None of these used cars is for sale.
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None of the police officers is out of uniform, sir.
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None of the ships at sea is sinking.
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None of the people using the Internet is sleeping.
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None of the hairs on your head is gray.
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None of our Christmas trees is dry.
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None of these houses is available.
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None of these sentences is correct.
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None of these dog's fleas is immune.
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None of these radio commercials is interesting.
Thank you for asking, Neil. I bet you timed out on this one!
According to my principle, when it comes to number, rather than amount, none is never more than one. None is always less than one. Therefore it requires a singular verb.
The first example should read:
None of the US presidents is a woman. Not None of the US presidents are women, or is women.
So, yes they are all properly rendered with the singular verb, "is".