Problem: We solve a problem. We get problems in math class to solve. Problems are solved by following the rules of a formal mathematical proof: induction or deduction.
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samerrustomCan I say " I am a facing a problem with my coworkers"?Yes.
samerrustomCan I say " I am a facing an issue with my coworkers"?It's unnatural. "Problem" is better.
samerrustom Is there any similarity between trouble and issue or problem?Absolutely, yes. But native English speakers use them in different contexts, and there are contexts where one or more of them could be used.