Final answer:
The first sentence is correctly punctuated without a comma between 'train' and 'that'.
Step-by-step explanation:
The correctly punctuated sentence is: The train that is taking us to New York has a full restaurant in the last car. In this sentence, the relative clause 'that is taking us to New York' is essential to identify which train is being referred to. Therefore, no comma is needed to separate the relative clause from the main clause. On the other hand, the second sentence with the comma between 'train' and 'that' creates a non-essential or non-defining relative clause, providing additional information about the train but not necessary for its identification. Therefore, the correct punctuation is without the comma.
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