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Negative questions, in my experience, are fairly common in everyday speach. The questions themselves are easily understood, but not the responses.

Ĉu vi ne faris viajn hejmtaskojn?

Jes / Ne

If I finished my homework, should I use jes or ne? Logically ne should place a second negation to the phrase and therefore make it a positive statement. However, in my native native language (Swedish) I'd say no if I didn't to the homework. Maybe this is why I am confused.

Here are examples of similar questions:

Ĉu vi neniam faris viajn hejmtaskojn?

Ĉu vi faris neniujn el viaj hejmtaskoj?

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This is discussed in PMEG in section 22.4, under Jes kaj ne ĉe neaj demandoj.

There are two methods, the Western and Eastern. The Western system is the one you are used to; the Eastern system is the strictly logical one.

Both are used in Esperanto; therefore, it is a good idea to respond with care to negative questions. However, the Western system predominates, and was the one generally (but not in every case) used by Zamenhof.

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Posting this answer here at the request of the asker:

Simply put, the answer depends on the expectations of the person you're talking to, so always strive to be clear and flexible.

A: Ĉu vi faris neniom da hejmtaskoj?

B1: Ne, mi faris neniom da hejmtaskoj.

B2: Jes, mi faris neniom da hejmtaskoj.

Both answers are OK.

You run into the same issue with dankon - which to some people means jes, dankon and to others it means ne, dankon. Always say either jes or ne.

A: Ĉu vi volas pomon?

B1: Jes, dankon.

B2: Ne, dankon.

B3: Dankon.

B1 Accepted the offer. B2 declined the offer. B3 was not clear.

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Very nice answers so far, it just seems no one discussed the situation if I wanted to say I actually did the homework (German doch / French si), so here's for completeness. In such situation, I would use a full answer, technically speaking with either jes or ne or maybe even neither, but supported by a ja:

Mi ja faris miajn hejmtaskojn.

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