It's a specific structure. In English you use [possessor] have/has, and in Russian it's У [possessor in Genitive] есть [noun in Nom.] or нет [noun in Gen.]. So, in this sentence the child is a possessor and he does not have a mother, so мама is in Genitive. Btw, мамЫ here is Gen.sing., not Nom.pl.
Damn! I should've just gone with the genitive as provided by http://starling.rinet.ru/cgi-bin/morphque.cgi?flags=endnnnnp for мамы. It sounded so much like мама, though, that I thought, naw, I got this. D'oh.
("Ребенок не с их матерью." I think? See Theron126 below)
Or "Ребенок не со своей матерью." see this:
Отец обязан обеспечивать удовлетворение финансовых потребностей своих детей, даже если они уже не живут со своей матерью.
The first sentence is different, it means "with their (plural, some other people's) mother. You can't use "их" for singular "their" in Russian, it would have to be "его", but that would again likely be understood as meaning someone else's mother. When the object belongs to the person who is the subject of the sentence, it is correct to use "свой", so you're right the second time.
Oh, I never considered that "their" could be singular. I stumbled across the second one accidentally. So the second one turns out to mean "his own" in this case and would be correct for the above lesson sentence, although it could also mean "their own"? and the first sentence actually does mean "their" which is plural and could be interpreted from Strabonis' sentence? In English, there is a third possibility "their" could include several children who are siblings and it could then be that the child is one of those siblings and it is his mother as well as theirs. For example, "Where are the rest of them? They are with their mother, but he is not with their mother." Although I would still be more likely to say "his" in that second part even if they share a mother.
You also can never use "его/ее/их" if you're referring to the person's thing to begin with, as then it implies that it's someone else's thing. You use the adjective свой to denote if it's the person's own thing. For instance, Муж ужинает со его женой would mean that he's having dinner with someone else's wife, but Муж ужинает со своей женой comfortably means that he's with his own wife eating dinner. As you can see, the connotations can be vastly different. Свой can be used in place of Мой, Твой, Наши, Ваши, also, but I'd say it's optional in those contexts since no one's going to be confused if I'm talking about my thing or my own thing.
ALSO... In common relationships you can usually just drop off the possessive adjective altogether since it's implied that if you're talking about a ребенок с мамой, it means that the child is with his or her own mother, not someone else's.
I think it's just because it's a preposition with such varied meanings and I don't think they can go through each sentence individually and specify its meaning in each exact sentence. Based on my DL experience, it just uses whatever definition(s) is/are given for the word and displays that in each sentence.
Ye/E is used presumably because in printed Russian ё is printed as an e anyway, and to possibly avoid confusion with ио or ыо.
Well at any rate I'm not trying to debate which system is better than another one or more logical than another one, just trying to point out that I assume the more options a computer can accept, the less accurate it becomes in "checking" answers.
ребёнок (Nom. Sing.) ends in a consonant, so it´s masc. "Y" in the sense of possession makes it Genitive: Masc. Gen. Sing. adds "a".
- Thus sorta regular in the sense that it ends with "a" but does a weird habberdash in the middle: Gen. Sing. ребёнка (rather than ребёнoка, which would be the result of a strict application of the rule).
- But, on a side note, definitely irregular in the Nom. Plu. ребя́та (rather than ребёнoкы ) and in the Acc. Plu. of the animate object ребя́т (rather than ребёнoкoв).
мамa is probably the Nom. Sing. form, as mother is most likely fem.
Fem. Gen. Sing. replaces "а" with "ы".
Helpful tables for Russian declensions: