Given the sentence "John told neither the boss nor the secretary.", which of the following has the same meaning?
- John did not tell both the boss and the secretary.
- John did not tell either the boss and the secretary.
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The model sentence is clear
John told neither the boss nor the secretary.
[He did not tell either of them.]
The first option is conjuntive.
John did not tell the boss and the secretary.
[He may have told one or the other.]
[He may have told neither.]
[He did not tell both]
The second option is grammatically incorrect since either should not be paired with and.
Technically, there is a small difference between 1 & 2
John did not tell either the boss or the secretary
is clearly what is intended (Or "John told neither the boss nor the secretary" which is equivalent.)
In this case:
John did not tell both the boss and the secretary
will most likely be heard as intended - if un-idiomatically - and as above
John did not tell (both the boss and the secretary)
Technically, however, one could tell the boss, tell the secretary, but not the two of them together. Like a 4-year old they could say "you didn't say I could tell each one individually!"
As such, only a grammatical laywer would ever come up with that intrepretation, but technically it is possible.
That said, #2 is by far the preferred way of saying it.
Either goes with or, and not and, so that makes 2 ungrammatical.
John did not tell both the boss and the secretary means that John said nothing to the boss and nothing to the secretary, just as John told neither the boss nor the secretary does. However, the first of those two would be unlikely to occur on its own. It would normally be part of a longer sentence such as John did not tell both the boss and the secretary at the same time, and, even there, both would probably come before at the same time, rather than before the boss and the secretary.