A2
てもいい — may, and it’s fine if
How Japanese grants permission with てもいい, refuses it with てはいけない, and asks for it politely.
The て form plus もいい. Literally even doing it, it is good.
ここに座ってもいいですか。
Koko ni suwatte mo ii desu ka.
May I sit here?
帰ってもいいです。
Kaette mo ii desu.
You may go home.
いい can be replaced by 大丈夫 or 構いません with no change of meaning, only of register: 構いません is markedly more formal.
Asking rather than granting
Stated flatly, てもいいです grants permission — which assumes you are the one with authority to grant it. As a question it asks, and that is how it is usually used.
写真を撮ってもいいですか。
Shashin o totte mo ii desu ka.
Is it all right if I take a photograph?
Refusing
てはいけない is the prohibition, built the same way with は instead of も: doing it is no good.
ここでタバコを吸ってはいけません。
Koko de tabako o sutte wa ikemasen.
You must not smoke here.
It is strong — the language of signs, rules and telling children off. Between adults a refusal is usually softened instead: ちょっと…, or a sentence left hanging on けど.
すみません、吸ってはいけません。
すみません、ここはちょっと…
Grammatically fine and socially heavy. Turning down a stranger with いけません sounds like invoking a rule at them; the unfinished version is the ordinary way to refuse.
Not having to
なくてもいい is the same pattern on a negative: even not doing it, it is good.
全部食べなくてもいいですよ。
Zenbu tabenakute mo ii desu yo.
You don’t have to finish it.
Note how neatly the set fits together: てもいい permits, てはいけない forbids, なくてもいい excuses, and なければいけない obliges.