Prepositions used after нельзя

Question

I encountered an example on Rosetta Stone which contrasted these three sentences:

1. Здесь нельзя с собакой
2. Здесь нельзя на машине
3. Здесь нельзя в туфлях

My question is, is there any grammatical reason why to use any of these pronouns and not the others? Are these specific to the noun just as в школе and на почте have pronouns specific to that noun? Or would нельзя в собаке also be just fine?

Answer 1

which contrasted these three sentences

All these sentences have some verb omitted. As we assume these verbs to be different, we naturally have to put different prepositions after them.

[гулять] с собакой --> [walk] with a dog
[ездить] на машине --> [drive] a car (no prepostion needed in English)
[ходить] в туфлях --> [walk] in shoes
[???] в собаке --> [what???] inside a dog

.

Are these specific to the noun

Specific to both a noun and a verb. I.e. just as usual.

Answer 2

Russian language often drops/omits the verb "to be." In all of the provided examples the verb "to be" (быть) is dropped.

Здесь нельзя [быть] с собакой

Здесь нельзя [быть] на машине

Здесь нельзя [быть] в туфлях

The choice of a preposition is dictated by how to be is connected with the object.

to be with a dog - быть с собакой

to be in a car - быть на машине

to be in shoes - быть в туфлях