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.