C'est impossible. - Si!
Je ne peux pas - Si! (I can't - yes, you can!)
English used to have a system with four words for that purpose [1].An interesting fact is that some early Gallo-Romance languages were named after the "yes" word in that language: langue d'{oc, oïl}. One can recognise oïl as a precursor for oui [2,3]
[1] https://en.wikipedia.org/wiki/Yes_and_no#The_Early_English_f... (cases with three forms such as French are detailled bellow).