Could you tell me how to use "live up" in different sentences?
The "up" in live up is a directional word. It is used because the Islands are at the top of the British Isles. At it's most Northern point, so it is considered up. "Live up" here is not being used as a phrasal verb or an idiom. You could replace up with another directional word if referring to another place and the sentence would still be correct. Ex: If you live down here, you can take a train. Ex: If you live over here, you have to drive. Ex: If you live near here, you can walk home.
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