"lubić" takes Accusative (as most of the verbs learnt in the first stage of the course), and if we negate Accusative, it turns into Genitive. This is the only case that changes when negated, others just stay the same.
"tamtej" is Genitive of "tamta", the feminine version of "that".
So to add up:
Lubie tamta kobieta (singular, accusative)
Lubie tamte kobiety (plural, accusative)
Nie lubie tamtej kobiety (singular, genitive)
Nie lubie tych kobiet (plural, genitive) (although I haven't heard of this form yet ;))
Pff... just as I got the hang of the first three, the last one is just so unlike the others ;)
It's pretty much true (although the actual border between the determiners for each set of distances is running at slightly different place, with Polish using determiners for closer distances more often than English). Is there a context to your question? Have you seen somebody who would use „tej” here instead?
I learned to speak Polish growing up, but I never learned proper grammar nor how to write, thus a lot of my understanding of Polish grammar I've gleaned from listening to conversations. I've always thought the distinction between these two words was "This" vs. "That," but doing some of the lessons here have made me question that assumption. Personally I would also use "tamtej" here, but from what I understand, "tej" would also be perfectly valid?
Edit: Thanks for taking the time to answer, by the way!
You mean whether „tej” or „tamtej” is grammatically correct in this sentence (disregarding the translation)? Yes, both can be correct, it depends on how far away the woman in question is. Isn't it just how "this" and "that" work in English? The only difference is that there is a certain set, where Polish would still use "ten" (this), when English would already use "that" (tamten). I can't recall an example when it would be the other way around, with English still using "this" and Polish already going into "tamten".
Yes, that was my question. It was simply that Duolingo will accept either as valid, but will translate both in the same manner (based on the implied distance of the object in question). I suppose I overlooked the fact that distance is not made especially obvious as these are written questions though, so the distinction must simply be dwarfed in the text. Thanks again!
"lubić" takes Accusative, true. However, when a sentence which needed Accusative is negated, it takes Genitive itself.
"Lubię tamtą kobietę" (Accusative), but "Nie lubię tamtej kobiety" (Genitive).
As people often spread this rule too far, I have to point out: Accusative is the only case that changes when negated. Other cases stay the same.
Well, cases are a very wide issue, so I advice to take a look here: https://www.duolingo.com/comment/16296174 and search for comments about cases.
Nominative is the basic, dictionary form. So it will mostly be used for the subject of the sentence, and also for both X and Y in an "X to Y" sentences.
Genitive is needed by some prepositions, by some verbs, but also when negating a sentence that needed Accusative. If you wrote "I like that woman", it's "Lubię tamtą kobietę". "lubić" takes Accusative, like almost all the verbs that you learn at the beginning of this course. So, when negated, it takes Genitive instead.
Don't spread this rule too far: only Accusative changes case when negated, other cases stay the same.
I wrote: "I do not like this woman" which is wrong as I understand, because tamtej means "that". What I don't understand is, why the correct answer given by Dou is: "I don't like the woman." As i understood "this" - "tej" - and "that" - "tamtej" - are only used to point out which person/ item I mean. I can understand that "tej" can be translated with "the". As there are no articles in Polish. But why should "tamtey" be traslated in "the"?
"lubić" should be "to like", and "kochać" should be "to love".
With things other than people, if the sentence uses "kochać" we usually also accept "to adore" and its Polish equivalent "uwielbiać".
The only sentence with "tasty food" that I can find now has "They are cooking", so none of those. If you can find it and comment there, maybe we can find out if it was a mistake or if there's some specific reason for such a translation.
Your surname suggests that you may probably be a native/fluent in Russian. Unlike Russian, Polish distinguishes very clearly between loving and liking.
Some Polish people would agree, but for many others it feels perfectly okay to say "kocham" about food. Or football. Or woodworking. But I understand why you felt that. Anyway, whether it feels natural or not, "kocham jedzenie" denotes something stronger than just "I like food".