"The dog does not have water."
Translation:У собаки нет воды.
How would we know if its dog or dogs? Because isn't the genitive case of собакa the same as the plural form [собаки]?
it must be something you learn from habit and not something you think about. I think probably after learning russian, without thinking you will notice that the word doesn't look right and not know why. You will have this feeling because you will have seen enough words to know a pattern where ы never comes after those letters. So it's not as hard as it seems it just comes with practice
Because it is in genitive form. "у собаки" is "by the dog" and "у" will always want genitive. It is the same if you say there is no dog (or "none of dog").
СобакА ест - The dog (nom) is eating
МамА любит собакУ - Mum (nom) loves the dog (acc)
У мамЫ есть собакА - Mum (gen) has a dog (nom)
У мамЫ нет собакИ - Mum (gen) has no dog (gen)
nom = nominative; acc = accusative; gen = genitive
The dog went to genitive in the last example, because there was "none of dog". When there is none of something, that something will be in genitive.
In the subject sentence, both dog and water are in genitive, because it is "by the dog" "у собаки" and there is "no water" "нет воды"
Nominative singular is собака: the ending "a" makes the noun feminine. Genitive rule here: а ⇒ ы. Exceptions: "In Russian we never write ы after г, к, х, ж, ч, ш or щ. That is why feminine nouns ending in а will get и at the end in genitive: книга ⇒ книги." (https://www.russianforfree.com/grammar-of-russian-nouns-genitive.php).
Memonic: "Good King Xavier Joyously Chewed Shashlik - SCHmatz!" It makes sense ´cos the position of the mouth is completely different for the exceptions (pouty lips), as opposed to ы (wide, stretched grin). There just isn´t time to move from strained grin to pout, so you don´t: и can stay poutи!
есть means "there is" In this sentence, the dog has no water, so есть wouldn't be correct.
But it is not a mandatory word for this structure in any case. Sentences where the focus is not on having something, but on some quality of the thing that is had, will omit есть. For example: I have a new car. У меня новая машина.
This sentence is not about having a car, but having a NEW car, so есть is not needed.