"Mohamed's restaurant is expensive but good."
Translation:مَطْعَم مُحَمَّد غالي لٰكِنّ طَيِّب.
in Genitive relations between two words, the definite article is added to the second word, in the same way almost where you put ('s) in English. Examples:
the cop's car: سيارة الشرطي
the man's hat: قبعة الرجل
the woman's dress: ثوب المرأة
and so on. Here though, because "Mohammed" is a proper name, it is then defined on its own and we can't add "al" to it, of course. Hence, مطعم محمد .
If the restaurant is called "Mohammed" that would be apparent in the context as well as in the grammar.
In the case of the genitive (OF-relation) between two words, the definite article goes on the SECOND noun. However, if the name is a "title" of the restaurant, then the two words are considered one entity (and hence the definite article would go on the FIRST noun only). Of course when the situation does not recall the need for identification (like the case with proper names here), the two examples would be similar in appearance; That's why I said it would be apparent from context, and beside grammatical issues related to the structures but I don't want to take that bend (since Duolingo is not teaching much grammar and it might get complicated).
In the example of pet name for example, this might be more common somehow than naming a restaurant with proper names sort of (here at least, but I remember one restaurant called Abdul-Waháb here), and calling a pet is somehow similar to the structure in English in fact, to some extent:
- I saw Sara's bird: رأيتُ طائر سارة (ra2aytu 6á2ira sára).
- I saw Sara THE bird: رأيتُ الطائر سارة (ra2aytu AL-6aa2ira sára).
As you can see, whenever in English the noun (bird) gets identified with THE, so it does with AL in Arabic, but with difference in structure of course. This structure is somewhat specific for identification or categorization of objects or living things in general but we would not use it for restaurant for example (same in English, I wouldn't think a structure like I went to Mohammed The restaraunt is a normal structure). All in all, I think Arabic and English in this specific niche coincide a bit despite the differences in sentence structure and order.
The grammatical construction covered in this exercise ("Mohamed's restaurant") is called the idafah (lit. addition) - the English equivalent is simply the genitive construction. Now regarding your question, the first term of the idafah is never preceeded by the definite article. The definiteness of the second term is sufficient to make the whole idafah definite. The examples, mentioned in TJ's answer, are perfect in order to understand what I am talking about.
It should be لَكِنْ طيبٌ "lakin Tayyib(un)" or لَكِنَّهُ طيبٌ "lakinnahu Tayyib(un)" and is impossible if it is لكنّ طيب "laakinn Tayyib(un)" - I assume "laakinn" is عامية as I never hear before. Reason: لكنّ lakinna is من أخوات كان which تنصب المبتدأ وترفع الخبر (so it cannot be followed directly by the complement) while لكنْ lakin is a Harf, which is more flexible.
My apology for the Arabic terms, I've found difficulties to say something when I should translate them into English logics - also, I don't understand much what you have said here with English logic wording. Feel free to ask! :))
(Tayyib) can be translated to good, kind, and even delicious sometimes. But it would sound weird if you used this word to describe some car for example.
(Jayyid) is mostly used as good and generally it talks about the quality of something, being higher or simply "good". Using (Jayyid) with food in my opinion is not common; Probably it might mean a food is well-cooked? Or simply looks good? For a delicious food I would rather use شهي (šahiy) or لذيذ (laδeeδ) rather than (jayyid) or even (tayyib), even though (tayyib) is used indeed to describe delicious food but just to avoid ambiguity.
PS: I used Delta (δ), for the sound of TH as in THis in English.