Why are both denna kvinna and denna kvinnan correct?
Because both reflect how Swedes speak, although denna + definite noun is discouraged in formal writing.
I thought that was flat out wrong.
Svensk ordbok says it's acceptable in written texts that are "not overly formal". denna kvinna does sound a bit too formal for most occasions.
With den här though, only the definite form is possible.
What's the purpose for the "den här" alternative to "denna"?
Thanks for clarifying.
Could you say Vad håller den här kvinnan på med?
Why denna and not de här for this?
Because it's one woman and not many. You would say Vad gör de här kvinnorna? but that would, of course, not match the meaning of the English sentence.
In the previous question it was detta man and here it is denna kvinna. Any suggestions?
same question ......
I think Duo should be more lenient. After all we are not studying Sweish to write books. Just to get along in everyday conversation.