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1. How can you be sure that I haven't already done my homework?
2. How can you be sure that I haven't done my homework yet?
What's the difference in meaning between the above two sentences?
 
1. How can you be sure that I haven't already done my homework?
2. How can you be sure that I haven't done my homework yet?
What's the difference in meaning between the above two sentences?

It's not a difference in meaning in the way you're thinking. The difference lies in how and why the questions could be used.
 
As I said, either expresses the idea.

(Quoted from Gemini)​

In short: Sentence 1 argues that the homework might be done. Sentence 2 accepts that the homework is not done, but asks how the listener knew.

Nonsense. Both are asking the same thing "how can you be sure?" The phrasing of the rest is two ways of saying the same thing.
 
As I said, either expresses the idea.
Nonsense. Both are asking the same thing "how can you be sure?" The phrasing of the rest is two ways of saying the same thing.
Do the sentences below mean the same thing?
3. I haven't already finished my homework.
4. I haven't finished my homework yet.
 
3. I haven't already finished my homework.
3. is not natural.
But 1 is natural, isn't it?
1. How can you be sure that I haven't already done my homework?
 

(Quoted from Gemini)​

In short: Sentence 1 argues that the homework might be done. Sentence 2 accepts that the homework is not done, but asks how the listener knew.

Why are you telling us what Gemini says? Do you want us to rate the answer? You sometimes quote AI in your threads and it's sometimes not clear to me what you mean by doing so.
 
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Why not use "yet" in a negative clause as the sentence below?
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https://english.stackexchange.com/questions/413436/the-word-already-used-in-negative-sentences
I have found the answer to my own question!
The Cambridge Grammar of the English Language (p710) states that already "characteristically occurs in positive clauses". But it later notes:
(Still and) already are certainly not wholly excluded from falling within the scope of a negative, but they do so only under restricted conditions ... .
The Collins Cobuild English Grammar (p262) specifies three of these conditions with examples:
Note that 'already' cannot normally be used in negative statements, but can be used in negative if-clauses, negative questions and relative clauses.
  • Refer certain types of death to the coroner if this has not already been done.
  • What does it show us that we haven't already felt?
  • ... all peers who did not already belong to the Privy Council.
 
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