I asked this question a few days ago in "ESL General English Grammar Questions" but haven't got an answer. Can anybody here answer my question, please?

In which sentences is the article "the" used? And when can we drop "the"?
Is it possible to use the article "a" in some of these sentences?

1.He is (the) owner.
2.He is (the) boss.
3.He is (the) manager.
4.He is (the) President.
5.He is (the) chef (cook).

Thank you in advance.
The article (the or a/an) can be used in all of these, and usually is. You can omit it when you are referring to a specific title: He is (the) President.

Thank you very much, Mister Micawber.

Could you give me some other examples of specific titles?
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Thank you very much, Mister Micawber.

1. Could you give me some other examples of specific titles?

2. Which article is used in this sentence?

I'm a / the director for a trade company.
1-- Sports Director, Accounts Manager, Prime Minister, Officer, Captain, Chef, Superintendant, Principal, etc.

2-- It depends on how many directors the trading company has.
1. Are specific titles always written with capital letters?

2. Which preposition is better "for" or "of"?

He is the director for / of a trade company.
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Do NOT use a capital letter for titles unless it comes right before the person's name.

There's Mayor Micawber over there. But: There's Mr. Micawber. He's our mayor.
And I think that 'of' usually works better.