a. The German sports car and the German airplane are made by the same company.
b. The German sports car and airplane are made by the same company.
Since the two are separate entities, A is the correct one, right?
Both can be okay. "separate entities" is not necessarily important; you have to consider the context.
It depends on how many sports cars and airplanes you are talking about.
a. The man and woman decided not to see each other.
b. The man and the woman decided not to see each other.
Both are correct. There is only one man and one woman; you don't need the second "the".
The first one is wrong because the two are not in a group, right? What do you mean by not "in a group"? You are talking about both of them.
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