We need the か particle to form “or”. In its simplest form:

ちゃコーヒー。
Tea or coffee.

For more complicated structures, we have already seen the grammar when we looked at how to embed questions.

先生せんせいがやさしい、わかりません。
I don’t know if the teacher is kind.

All we’re doing now is adding another embedded question using the same grammar.

先生せんせいがやさしい、やさしくない、わかりません。
I don’t know if the teacher is kind or unkind.
チョコをはな、まだめていない。
I can’t decide whether to buy chocolate or flowers.
そのひと課長かちょう部長ぶちょうわからない。
I don’t know if she’s a departmental head or a divisional head.
裕輔ゆうすけ今週末こんしゅうまつは、友達ともだちとキャンプに行ってバーベキューするよ。
YusukeThis weekend I’m going camping with friends and will have a BBQ.
純子じゅんこそうなの?いいね。
JunkoReally? Nice!
裕輔ゆうすけまあ、それいえでのんびりする。
YusukeWell, either that or relax at home.

Just like when we looked at the casual form of a questions using na-adjectives and nouns, we may see なのか used instead of just か to form the structure.

これが鶏肉とりにくなのか牛肉ぎゅうにくなのか、ウエーターにこう。
Let’s ask the waiter whether this is chicken or beef.

Additionally, you may hear それとも used inside the question clause. This does not change the meaning, merely places emphasis on it being either A or B.

あれが飛行機ひこうきなのかそれともとりなのか、わからない。
I don’t know if that’s a bird or a plane.
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