In the book Faramir tells Frodo that Boromir is dead, and that leads them to think that the rest of their friends are too. Faramir says that maybe some of them did survive, because of the manner in which Boromir was laid out, but what he saw was only a vision so there is no reason for Frodo or Sam to think that any others of the Fellowship still live.
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"But after coming all that way I don't want to give up yet. It's not like me, somehow, if you understand."
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