In my experience, they are often used fairly interchangeably; although it isn't correct to do so. In all cases, you are thinking something is the case, the differences are: Assume - without proof Presume - based on probability Suppose - based on evidence or probability but without proof or certain knowledge
They also each have a second completely different definition. I'd never actually thought about the differences before (native English speaker).
I wrote "She supposes that we have fault." and it was marked wrong. Couldn't we use the noun part of speech of "fel", please? If not, then how shall we translate "She supposes that we have fault / mistake." ? And, must we use singular "a fault / a mistake" or plural forms "faults / mistakes" in Swedish and English? Tack tack. :)