"The woman sleeps on the bed."

Translation: Kvinden sover i sengen.

[niscate]

In English it is possible to say both "to sleep on a bed" and "to sleep in a bed". Is this not possible in Danish?

[DaneTR]

"(at) sove i en seng" would probably only be used for babies sleeping in specials beds. When one says so, it's considered that one's sleeping inside the bed which one probably isn't

[supainanoko]

Then why is it wrong to say ''kvinden sover på sengen''?

[runem]

"På sengen" would be "on top of the bed", in this case. Like, "I left the suitcase on the bed" would be "Jeg efterlod kufferten på sengen". When you go to bed, you are "i sengen".

DaneTRs answer makes me wonder if there are regional differences to this. Are you Danish, DaneTR? :)

In any case, both "på" and "i" are accepted now, since they're both correct translations of the English sentence.