Learn Hardcore Ukrainian: Ні я, ні моя сестра сьогодні не вільні.

Ні … ні … means “neither … nor …”. In Ukrainian, negative concord is the norm: when the subject (or another part) is negated with ні, the predicate is also negated with не. So you must keep не before вільні. Without не, the sentence would be ungrammatical or sound very odd.

Why is вільні in the plural?

Because the subject is compound: ні я, ні моя сестра refers to two people. In Ukrainian, a predicate adjective agrees in number with a compound subject, so you use the plural form вільні.

Where is the verb “to be”? Why isn’t there є?

In the present tense, Ukrainian usually drops the copula є (“to be”). Predicative sentences are formed as “Subject + predicate adjective/noun.” You can optionally include є for emphasis, contrast, or in formal style. If you do, many writers put the predicate in the instrumental case: Ні я, ні моя сестра сьогодні не є вільними. In everyday speech, the most natural version is the one you have, without є: … не вільні.

Is the comma after ні я required?

Yes. With repeated correlatives like ні … ні …, you separate the parts with a comma: Ні я, ні моя сестра … No extra comma is needed before не вільні. A dash is not required here.

Can I move сьогодні or change the order of the two subjects?

Yes. Ukrainian word order is flexible. These are all natural:

Сьогодні ні я, ні моя сестра не вільні.
Ні моя сестра, ні я сьогодні не вільні.
Ні я, ні моя сестра не вільні сьогодні. The meaning stays the same; you just shift emphasis slightly.

Why я (nominative) and моя сестра (nominative), not мене/мені or мою сестру?

They’re subjects, so they must be in the nominative case: я, моя сестра. The predicate adjective вільні also appears in the nominative (plural) to agree with the subject.

Why is it моя and not мій?

Because сестра is feminine. The possessive pronoun agrees with the noun’s gender and number:

masculine: мій брат
feminine: моя сестра
neuter: моє місто
plural: мої друзі

Could I use ані … ані … instead of ні … ні …?

Yes. Ані … ані … is a stylistic variant, often a bit more emphatic or formal. It works the same here and still requires не on the predicate: Ані я, ані моя сестра сьогодні не вільні.

Can I drop не and just say Ні я, ні моя сестра сьогодні вільні?

No. With ні … ні … used on the subject, you still need не on the predicate. Otherwise the sentence clashes logically and sounds incorrect. Keep не: … не вільні.

What’s the difference between не вільні and зайняті?

не вільні = “not free/available.” It’s neutral and simply denies being free.
зайняті = “busy/occupied,” implying you have commitments or are tied up. Often зайняті sounds more idiomatic when you mean “busy”: Сьогодні ми із сестрою зайняті. Both are correct; choose based on nuance.

Can ні … ні … be used with verbs or objects too?

Yes, but the mechanics change:

With verbs, ні usually attaches to each verb and you don’t add an extra не: Він ні їсть, ні спить.
With objects, you typically negate the predicate with не and put ні before each object: Я не люблю ні кави, ні чаю. In your sentence, ні … ні … targets the subject, so the predicate is negated with не.

If there were a finite verb, what person/number would it take with ні я, ні моя сестра?

Use the plural. Because the subject includes я (1st person), the verb would be 1st person plural: Ні я, ні моя сестра не маємо часу.
General guide:

Includes я → 1st person plural (не маємо).
Includes ти (but not я) → 2nd person plural (не маєте).
Neither я nor ти → 3rd person plural (не мають).

How would the form change with gender or number?

The plural adjective вільні is used for any mixed or same‑gender group. For a single speaker:

male: Я сьогодні не вільний.
female: Я сьогодні не вільна. Plural for any group: Ми сьогодні не вільні.

Is there a shorter, more colloquial way to say this?

Yes: Сьогодні ми з сестрою не вільні (literally “Today we with [my] sister are not free”). It’s very natural in speech and keeps the same meaning.