I can't understand why in this type of sentence an author doesn't use the article if we are talking about definite nouns ( head noun which modified by prepositional phrase). Portraits why without a definite article? here example The boy draw portraits of people why waiting for an aeroplane at the

Bogdan Bezfamilny
Hello, my apologies for having overlooked this question of yours that you asked so long ago. First, I believe you mean "while" and not "why" in your sentence and also either "draws," present tense or "drew," the irregular past tense of "draw." Plus I suspect the last word was omitted, that is, I believe your whole sentence is something like "The boy drew portraits of people why waiting for an aeroplane at the airport."
As to your specific question, the reason we don’t have the definite article "the" before the noun portraits is (1) it’s the first mention of the noun and (2) in the case of (1), for plural countable nouns like "portraits" from "portrait" we don’t use any article at all (though we could use "some" here, but again, no article is needed). Compare, for example, "The boy drew a portrait" where we must use the indefinite article "a" since "portrait" is singular, not plural.
So it is true that the noun "portraits" in your sentence is post-modified by a prepositional phrase ("of people") which normally requires the preceding noun to be definite (i.e., "the portraits" instead of just "portraits"), but the larger context of the sentence is what overrules this principle here, namely again that this is presumably the first mention of these portraits the boy is or was drawing, so we signal that by having no article before portraits; "The boy drew the portraits of people…," by contrast, would imply that the portraits have already been introduced and mentioned in the discourse, i.e., the conversation or the writing.

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