[Grammar] Do you think-questions and answers

[tyrp]

Hello,
Could you help me with the following. What is the correct way to agree with the speaker and confirm his/her statement in questions starting with "Do you know/think/etc" if they are followed by a negative information-giving clause?
E.g. Do you think Mary isn't Bob's girlfriend? - No, she's his sister (a). OR Yes, she's his sister (b)
If it were just a question, everything would be easy:
Isn't Mary Bob's girlfriend? - No, she's his sister.
But in "Do you know/think/etc"-questions does the "No"-component refer to the part with "know/think etc" or to the information provided in the clause?
I'm more than a bit perplexed.
Thanks a million for your help!

 

[emsr2d2]

In all honesty, if someone asked me "Do you think Mary isn't Bob's girlfriend?", I would think it was a strangely worded question. I probably would not reply with anything that started with "yes" or "no". I would reply with "Actually, I think she is" or "I think Susan is Bob's girlfriend".

 

[tyrp]

Thank you very much, dear emsr2d2. Could you tell me why you consider the question itself strange? Thanks again.

 

[Rover_KE]

It would take me a minute to get my head round what it meant. You'd have to give me time to think about it.

 

[Raymott]

Talking about which part the 'yes' or 'no' component of the answer refers to is not useful, because it has to followed by something.
'No' refers to "No, Mary is not Bob's girlfriend. She's his sister."
'Yes' refers to "Yes I do think that Mary is not Bob's girlfriend, because she's his sister."
But the answer is not likely to be just 'Yes' or 'No', so it doesn't matter. The information you want comes after any "Yes/no", which tells nothing by itself.
In strict grammar the "Yes/no" would refer to "Do you think ...?", but it doesn't work that way pragmatically.