"Our cat and her dog"
Translation:Nasz kot i jej pies
Well, an alternative is to learn as children, who don't know or care about cases, do. They just learn by osmosis :-).
Consider these English sentences:
I have a dog. I have dogs. The dog is eating. This animal is a dog. These animals are dogs. The dogs are eating.
These are equivalent to these Polish sentences:
Mam psa. Mam psy. Pies je. To zwierzę jest psem. Te zwierzęta są psami. Psy jedzą.
If you can learn these, then that's a start. You could also look at https://en.wiktionary.org/wiki/pies#Noun_5 and click on "Declension of Pies" to see what is going on.
Looks like there are a few exercises, like this one, that don't focus on the subject covered in the lesson. In this case, the differences between the options are just the last words (radio, pies, kobieta). This puts the focus of the exercise on knowing the meaning of those three words. However, this lesson is about pronouns, so it seems like the exercise could be improved by putting the focus on the pronouns, rather than on those other words that were already taught in previous lessons.
Hmm, looks like I'm not explaining very well what I mean. In this exercise you have to choose among three sentences that are all the same except for the last word (radio, pies, kobieta). That means that in order to complete the exercise you just need to know the meaning of these three words. You can do the exercise right even if you don't understand any other word in the sentence, because the other words are all the same in the three options. But that is not the goal of this exercise, its goal is to make sure that we know the pronouns. In order to achieve that we need an exercise where the difference between the options are the pronouns. For instance, an exercise that has "nasz" in the first option, "jego" in the second, and "ich" in the third.
Does it make sense now?
And, if I understand the question of morethanafeelin correctly,
in "Nasz kot i jej pies" the pronoun "jej" doesn't refer to the dog being owned by a female cat, but to the dog being owned by a female person. The genders of the animals are not specified.
in "Nasza kotka i jej pies" the cat is female and without any context you actually should assume that "jej" refers to the dog being owned by a female cat. Of course one animal is usually not owned by another and with a context it would be usually clear that you mean something else (e.g. "Lubimy Ewę. Nasza kotka i jej pies też się lubią" = "We like Ewa. Our [female] cat and her [i.e. Ewa's] dog also like each other").
Because the dog has a different grammatical function in those sentences. OK, what we have here isn't even a sentence but a phrase, but let's say that it's "Our cat and her dog are eating". "her dog" is a part of the grammatical subject, so it takes the basic, Nominative form, which is "pies".
In "I have her dog", "her dog" is the direct object of the sentence, so it takes the Accusative case, which is "psa".
In English you almost don't have cases, but this difference is visible if you imagine "He is eating" vs "I like him". "he" and "him" mean exactly the same, but the words use different forms. That's what's left in English from the case system it also used to have (centuries ago).