Well this seems not a grammar question but yeah I think you are right.
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AnonymousEven if the conversation partner doesn't know which library I'm talking about or how many libraries my town has, is that answer correct? My town has only one library.In your case, with only one library in town, 'the' is the only possible choice.
btan2893Well this seems not a grammar questionA question about whether or not to use the definite articeleseems to me to be a question about grammar.