I want to ask about two sentences, and what would be the correct way to form a question:
It's very important that we eat healthy food, ...........?
Which would be the correct question tag: (isn't it) or (don't we)?
It's a must that all applicants follow the rules of the competition, ..........?
Which would the correct question tag: (don't they) or (mustn't they)?
Please could you tell me the correct answers, and, more importantly, why those are correct?
For the first example, isn't it is correct. Don't we does not make sense in this context. The sentence should be:
It's very important that we eat healthy food, isn't it?
The second example, I would not use either option. Instead, I would use isn't it here as well:
It's a must that all applicants follow the rules of the competition, isn't it?
The reasoning for this is that it coincides with the beginning of the sentence. For example, I might use any of these:
They should eat healthy food, shouldn't they?
There are a lot of people here, aren't there?
You are connected to the Internet, aren't you?
Don't and didn't are exceptions to this:
You have an Internet connection, don't you?
He came to work yesterday, didn't he?
As other answers indicate, it's quite straightforward that in these specific cases, the only acceptable "question tag" is isn't it? It would be much more incisive (and more awkward) if OP's example had been:
It's important that we should eat healthy food, ...........?
That still wouldn't change the fact that technically speaking, isn't it is still the only "correct" tag, but in practice many/most native speakers wouldn't see anything odd about using shouldn't we there.
As an example of how ridiculous things can become when people try to force "strictly logical" constraints on the "subject" of a question tag, consider this sentence:
All I meant was that he should have seen it, shouldn't he?”
Those very same "strict rules" that require isn't it for OP's example would force us to accept that the only valid tag for my example must be didn't I. It probably wouldn't raise an eyebrow among native speakers if you did use the "valid" form, but unquestionably the version as written would be far more common.
In short, there is a vague area hereabouts, since meaning affects question tag format as much as, if not more than "grammatical rules". In most cases, the question tag agrees with the initial subject/verb. But if there's a more semantically significant "secondary" possibility, it's often acceptable to target that instead.
In the first sentence, it should be
It's very important that we eat healthy food, isn't it?
One problem is that the subject of the first clause "it" does not specify what "it" is, though it should say in context. If you say
To stay healthy, it's very important that we eat healthy food, isn't it?
Since we are talking about health, its a state, not an action. So "isn't it" is appropriate.
In the second sentence, again it depends on what "it" is. If you say
In this competition, it's a must that all applicants follow the rules of the competition, isn't it?
"Competition" is an event but not an action, so "don't they" or "mustn't they" are incorrect.
