Negation – How to Answer with ‘Yes’ or ‘No’ When It’s Not Working

The basic (declarative) sentence is:

He does not know.

You can turn this into an interrogative clause with subject-auxiliary inversion. Just switch he and does:

Does he not know?

You can optionally replace does not with doesn't in the original sentence, using the suffix -n't rather than the word not:

He doesn't know.

Now the auxiliary is the single word doesn't, so if we apply subject-auxiliary inversion, we get:

Doesn't he know?

Lastly, you can turn the original sentence into a question by using rising intonation at the end, which you indicate in writing by replacing the period . with a question mark ?:

He does not know?

However, this is only appropriate in certain situations, for example as an echo question—repeating what you heard as a question to express incredulity or to confirm that you heard the speaker correctly. Most (but not all) situations where this would be appropriate are informal, and as a result "He does not know?" sounds somewhat unusual. Instead, you can use the contracted form:

He doesn't know?

But most of the time the interrogative form is more appropriate.

The sentence (A) isn't correct grammatically.

"I couldn't open the door" is in the past. As a matter of fact, you are locked in and unable to open the door at the present time. So the correct sentence should be:

I am locked in here and cannot open the door. Can you help me?

The second sentence (B), which is in the past, is correct grammatically. Could is the past of can.