Hfrhyu

I'm doing some homework, in which we have pictures and we have to complete the sentences like "Ist das ein Salat?" - "Nein, das ist kein Salat. Das ist ein Bus."

In the example above, both Salat and Bus get the article "ein", so I get why the answer is "das ist". But Nase is feminine, so it gets "eine". Why it is correct to say "Das ist eine Nase", and not "Die ist eine Nase"?

In German language, the word "das" is not only an article. It has a second meaning:

It can also have the meanings of the English words "this" or "that".

If the word "das" means "this", there are no different words for male, female and neuter but there is only one word: "das".

In your sentence, the word "das" is not used as article but it means "this".

By the way:

The word "der" sometimes has the meaning: "this man" and the word "die" sometimes has the meaning "this woman".

So the sentence: "Die ist eine Nase." would mean: "This woman is a nose."

Articles can also refer to a word in a sentence before:

Auf diesen Bildern sind Teile des Körpers zu sehen. Der hier ist eine Nase.

In this case, "der" would be an abbreviation of "dieser Teil" ("this part"). The gender (der/die/das") would be specified by the gender of the word "Teil" in this case and not by the gender of the word "Nase".

Quite as in English:

That's a house. That's a beer. That's a girl. That's a boy. That's a nose. That's a leg. That's a liver. That's a stallion. That's a mare. That's a flower. That's a ship.

Genus just does not play a role here. (Nor does sex.)

Note that by tradition, ships in English are referred to as females:

That's the Queen Mary. The Queen Mary is 300 metres long. She (!) has four chimneys.

Theoretical explanation: You can see the Das as the equivalent of the English That: as a demonstrative pronoun, not as an indicator of genus. Under this perspective, the das here is a different das than in der, die, das. But that's really a theoretical consideration with not too much relevance for using the language in everyday life. For everyday life you simple get used to saying Das ist eine Frau although the Frau is female by genus (and probably also by sex).

Note additionally perhaps:

That's milk.

Yeah, you do not count milk, and in these cases you go without the definite article. Same in German:

Das ist Milch.

But:

Das ist ein Glas Milch.

The answer is pretty simple, because das explicitly doesn't refer to the nose that was in context. This "das" is an indefinite pronoun and thus does not receive a gender, but defaults to neutral, inanimate gender. We might also use "dies", "es", or even "so-etwas" ("Sowas ist doch nicht normal").

If talkling about people instead, we would make a difference, "Nein, Sie ist keine Nase", and we might use gendered articles as pronouns, too, e.g. "die", shortened from "die Frau", or "Der ist so schlau, der vectory".

We only refer to a specific gender, if it's already in context, but it just doesn't work well with negatives. Hence:

Das ist gar keine Frage

Das ist ja wohl unerhört

Vice-versa, we may use the indefinite pronoun for positive statements, pretty much by analogy

Ja, das ist ein Golden-Retriever

Which is unproblematic because in most cases we could surmise a neutral noun to fit, e.g. "das Tier".

Further:

dies seems to be a mix of both die and das, in case you can't decide :) but we also have the anaphoras "dies und das", and "dieses und jenes".

es actually stems from a meaning "here".

Combining both we get dieses ist keine Nase (which sounds a bit like ellipses of dieses Ding). We would not say diese (female) in such cases, however.

etwas--I found nothing concrete about it--may by my estimate be in part from es, PGmc *hit "that", PIE *ke-, *key- "this, here", too, bound with "was" cp. "Ich habe hier etwas", "look at this here".