Student or Learner
I went to a/ the supermarket to buy some bread, but it was closed.
In the case above, which article would sound more natural?
I think a supermarket sounds logical if you have more than one choice of supermarket in your mind. However, it seems to me the supermarket is normally used even if there's more than one choice.
In general, "the supermarket" is thought of as a resource, still with the understanding there is more than one close by or in the area.
I'm going to the supermarket?
Which one are you going to?
Saying something like "I'm going to a supermarket" is strange even though it's grammatically correct.
In an unfamiliar area, you could say, "I wonder if there's a supermarket close by". Or asking for information, you could say, "Is there a supermarket around here?".
specific supermarket - Can you tell me where the nearest supermarket is?