Hi
As English is very specific in use of negative forms I often have difficulties with… logic. 
‘Did you not <some action, for example, “tell her”>’?
‘Certainly, we did’.
–> ‘We’ told her or not?
‘Did you not tell her ?’
‘Certainly, we did’.
If we told:
“Certainly, we did”, or “Yes, we did”, “We did, certainly”
If we didn’t tell he: “Certainly not”, or “We certainly did not”.
In each case “tell her” is implied after “did” or “did not”.
.
In English, the response agrees with the truth, Tamara, not with the question’s polarity:
Did you tell her? – No.
Didn’t you tell her? – No.
You told her? – No.
You didn’t tell her? – No. In all these she was not told.
.
Hmm, how interesting… I mean – independency from (polarity of) a question.
I didn’t know that. And supposedly misinterpreted other’s speaking and made mistakes with my own answers (but who knows?… :))
So, now I can surely give the correct answer even before the question will be asked – what a great language, indeed!
Just always answer the truth… or always tell the lie. – the simplest rule of thumb.
Thank you!