"when was he a teacher?"
"when wasn't he a teacher?"
"when is he a teacher?"
"when isn't he a teacher?"
Are these questions grammatical and idiomatic?
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They're grammatical but they carry a wide range of meanings.
"when was he a teacher?" =when (in the past) did he teach as a profession?
"when wasn't he a teacher?" Implies that during his entire life, he tried to teach things to people- a calling rather than a profession
"when is he a teacher?" NOt a common usage, or smooth. If you had someone who is professionally a teacher but spends all his time doing other things, such as political or social activities, you're asking "Does he take any time to actually teach instead of trying to make political progress with the principal?"
"when isn't he a teacher?" Would be said of someone who 'can't turn it off.' They teach professionally, but are always seeking to educate others, in a positive or negative sense.
[W]hen was he a teacher?"
"[W]hen wasn't he a teacher?"
"[W]hen is he a teacher?"
"[W]hen isn't he a teacher?"
This may be an exchange between 2 people on a 3rd person. For easy explanation, I use the term 'candidate' to refer to that 3rd person.
In (1), the candidate was or might have been, but is no longer, a teacher.
Scenario 1 The question may be asking in a straightforward manner for the period of time the candidate was a teacher.
Scenario 2 If this is a conversation, and if there is a doubt about the authenticity of the candidate's claim of having been a teacher, with appropriate tone, this line may be used as a query to express that doubt.
In (2), there was a period in the past the candidate was not a teacher. Similar to scenario 1 described above, this can be a query for that period of time.
(3) seems quite rare but may be used in a situation of someone having different professions in different parts of the year. Similar to scenario 1, this asks for the period of time the candidate works as a teacher.
(4) is similar to (3) but is asking for the reverse.