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These sentences are from some data set used for evaluating programs that automatically process languages, but I am doubtful about their grammaticality.

(1) A man and woman are talking
(2) The boy and girl are not playing on a playground.

I guess they should be written as (1a) and (2a):

(1a) A man and a woman are talking
(2a) The boy and the girl are not playing on a playground.

Otherwise the noun phrase of form 'Det N1 and N2' will talk about things that are N1 and N2 at the same time, like in (3,4). Am I right?

(3) The student and artist is sleeping.
(4) Every student and artist is smart.
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    When you say "a student and artist are", the plural verb keeps it from being interpreted as a single person who is both a student and artist. For "a man and woman are", it's both the plural verb and common sense. You can get ambiguity, as in "I met a student and artist in the park yesterday," but only one of your sentences is ambiguous. (Every student and artist is smart.) And even if they were ambiguous, they would still be grammatical, although it would be a good idea to reword them to remove the ambiguity.
    – Peter Shor
    Commented Dec 22, 2014 at 13:07
  • Then you will have unambiguous and grammatical sentences.
    – Edwin Ashworth
    Commented Dec 22, 2014 at 14:11
  • @PeterShor At that rate, most grammatical rules can be left by the wayside, as we do in conversation anyway.
    – Kris
    Commented Dec 22, 2014 at 15:31
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    @Kris: Exactly what grammatical rule is being broken by "A man and woman are ..." If there is one, it's not one that most native English speakers follow. See Ngram.
    – Peter Shor
    Commented Dec 22, 2014 at 15:33
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    Non-native speakers should be cautioned not to take what their textbook says about articles seriously. Article use is virtually all idiomatic; there is no "rule". There are several hundred rules, all different.
    – John Lawler
    Commented Dec 22, 2014 at 15:38

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The comments boil down to this: there is nothing ungrammatical, nor ambiguous, about your initial examples (1) and (2). The articles can be dropped without losing meaning. And your conjecture that the structure implies someone is simultaneously a man and a woman, or a girl and a boy, and is talking (or playing, respectively) with itself is absurd. True, articles would help when you talk about "a student and an artist", but I would remind you that even this phrasing does not unambiguously point to two separate people; one can say: "He is a student and an artist."

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