prove that for all real numbers x and y, if x+y ?= 2, then either x >=1 or y>=1

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prove that for all real numbers x and y, if x+y ?= 2, then either x >=1 or y>=1

Mathematics
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I mean if x+y >= 2,
Ok, one way to prove this would be by considering different cases. So first try and see what would happen if you assumed that x <= 1
can you please tell me the whole thing? I don't know how to solve it at all.

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