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What is the difference between these two pertaining an activity that is not covered or already covered.

I believe I haven't already covered this global warming topic. (Teacher)

Vs.

I believe I haven't covered this global warming topic yet. (Teacher)

Is there any difference? Such as the time it played out or something?

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When 'already' is used with negation, it most likely emphasizes that something should have happened by the moment.

'Not yet' is a neutral expression for something expected to happen soon.

https://dictionary.cambridge.org/grammar/british-grammar/already-still-or-yet

(Negatives with already are far less common than negatives with yet... They usually refer to things which should have happened before they did happen)

So in your first example the teacher probably planned to cover that topic by the moment, in the second one the time for the teacher's explanation has not come yet.

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