Consider this scenarios:
A: Can I do X?
A: Can't I do X?
In both the cases, the B replies with "Yes" to indicate A can do X and with "No" to indicate he cannot.
The 1st one seems to ask for permission while the 2nd one seems to imply a tone of indignation.
Consider another scenario:
A: Can I not do X?
A: Can't I not do X?
Here, B replies with "Yes" to indicate A doesn't have to do X and with "No" to indicate A has to.
Here also, the difference is subtle: A seems to just ask for clarification or permission in the 1st and seems frustrated or even resigned in the 2nd.
My question is, what are the differences between the 2 then?