expression
won't; hasn't; isn't; doesn't
Polite negative question used to ask whether something is not the case. Often expects confirmation or expresses surprise.
See also: ます
この電車は東京に行きませんか。
Doesn't this train go to Tokyo?
まだ宿題を終わっていませんか。
Haven't you finished your homework yet?
expression
won't you; shall we; why don't we
Polite invitation, suggestion, or indirect command. Softens a request by framing it as a negative question.
一緒に映画を見に行きませんか。
Won't you go see a movie with me?
そろそろ出かけませんか。
Shall we get going soon?