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Does "to live (together) with someone" necessarily mean "to live (together) with someone in the same house"? Isn't it possible for it to mean something about close relationships with someone or standing by someone's side, always being with him/her while living?
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Live with someone normally means in the same house. I would not expect it to be used to mean spend a lot of time together.
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I see. But "live without someone" is not necessarily about living without someone in the same hose, is it?

(e.g. I cannot live without her)
That's true. English is funny that way. Emotion: smile
Look at your own parentheses Emotion: wink In "live without them", there is no "(together)", true? That said, you're right that both uses exist:
Lived (together) with them (in the same house)
Could not live without...
[and also]
I can live with (tolerate) that.
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Blue JayThat's true. English is funny that way.
Indeed.