Translation:No, there are no pets.
"It is not a pet" (i.e. it is something else than a pet) would be ペットはじゃないです.
います and いません mean "there is / there is not" (for living things), while です and じゃないです or じゃありません mean "it is / it is not".
The last word above is not to be confused with あります ("there is" for non-living things) and it's negative form ありません. Well, it certainly confused me. ;)
Yeah, i almost pluralized my answer, but started to question myself. Sometimes i like to be a jerk and say things like "there are 5 ninja in the tree." or "i have watched 200 anime." just to make my fellow Americans squirm from the lack of an "S." Usually, no one cares or notices...
Yes, generally you do. That's because が indicates the subject, or the thing which does the verb.
However, as Tanja rightly points out, は is often used with their negative forms to add emphasis.
This is possible because は is not simply the topic particle, but it can also be the topic particle plus the role of whatever particle it replaces, in this case が. In earlier exercises, we saw 「お茶は飲みません」 where は took over the role of を for added emphasis.
But in this case, without a proper context, you cannot say if this sentence is "There are no pets" or "I dont have pets". If we translate as literal as possible, it should be "there are no pets" , while for "I dont have pets" would be "ペットは持っていません". Another story would be if we have a context.
飼っている is one way to talk about having/owning pets. As @Alcedo-Atthis said, using just いる/います is common in Japanese.
In fact, just using いる is probably the more natural of the two. The connotation of it is that you consider your pet as part of your family (because that's how you would describe your family members), so it seems more endearing than 飼っている which seems to emphasize your responsibility (as the owner) for the pet. I might be reading a little too much into it since I'm not a native speaker, but both verbs are equally correct.
You can only use が for います and あります, and not を. However, は is a bit of an exception, because it can indicate the topic and fulfill the grammatical role of a particle it replaces, which you can do for emphasis. We've seen this before in other exercises, like おちゃはのみません.
So in this case, は is kind of は and が at the same time.
Although it's not incorrect, that has the implication of "I'm not carrying a pet with me right now". It's similar to this example:
A: "Can I borrow a pen?" ペンを貸してくれませんか？
B: "No, I don't have a pen on me" いいえ、今、ペンは持っていません。
To say "I don't have a pet" and mean "I don't own a pet", you could simply say the exercise sentence (ペットはいません), or to be more specific, you could say ペットは飼(か)っていません, where 飼っていません means "to not currently keep/feed (an animal)"
Aye, いません is used for living creatures, but with ペットではありません we're talking about something that is clearly not a pet. (says so in the statement after all!) :)
Jokes aside, ペット is a regular noun with no 'living or dead' distinction required in this case. ではありません is the formal negation of です, which is the auxiliary verb "to be" (i.e. "to be something", not the existential "to be or not to be" kind). So the positive version of this sentence, "that is a pet", would be ペットです, not ペットはいます (since that means "there is/are (a) pet(s)").
The Japanese is a person presumably answering a yes/no question. "No, there aren't any pets." When you don't translate the いいえ, you're changing the meaning of the sentence.
いいえ、ペットはいません。 (iie, petto wa imasen)
No, there aren't any pets.
ペットはいません。 (petto wa imasen)
There aren't any pets. / There are no pets.
I'm not sure I'm understanding this correctly after reading what others said, but from what I was taught growing up and in school, you can only use います if the subject is a living thing (animal or human) and あります if it is inanimate. Therefore saying ペットはありません kind of sounds like you are saying your pet is dead or imaginary
Yup, you're mostly right. As a general rule of thumb the living/non-living divide is pretty close to animate/inanimate, but it's not quite the same.
います/あります follows the animate/inanimate line of thinking, so things like plants (which are living but inanimate) use あります, and zombies (which are animate but non-living) use います.
However, rather than sounding like your pet is dead or imaginary, ペットはありません just sounds ungrammatical because anything you would have as a pet is generally animate (or would be described in an animate way, e.g. a pet rock).
No, は indicates that "pet" is the topic of the sentence. Arguably though, "no pet is there" is a pretty close translation for ペットはいません, which I would probably accept.
However, the sentence in this exercise is 「
いいえ、ペットはいません」so you would have to say "
no, no pet is there", which makes it sound considerably less natural in English.
For me as a native speaker, if the sentence was something like "there's no pets allowed", I hear what you're saying, but to say "there's no pets in the house" sounds wrong to my ear, which would be more the context that this sentence is using. Maybe we speak different dialects.
It's not something you need to worry about too much as a beginner. Suffice it to say that が (usually) indicates the "subject" or the "doer" of the verb in the sentence, and は can also do this to add emphasis (by elevating the "subject" to the "topic" of the sentence). This often happens for negatives and questions.
If you really want to find out more, check out Tae Kim's Guides among other useful resources on le Google.
MelSuwako asked a similar question if you check the previous comments: https://forum.duolingo.com/comment/23114473?comment_id=32087252