In a quiz, there was a question asking students to show something doesn’t exist. A lot of them gave proofs by contradiction.
Initially, I designed the marking scheme so that an incomplete proof by contradiction would lead to 0 marks, because I thought that exhausting all cases is very important in a proof by contradiction. Otherwise, there may not be any contradiction at all (another case is valid). Some students may impose an (perhaps, obviously contradictory) assumption and claim that their proofs are complete.
However, I found that a lot of students missed some cases, or imposed extra assumptions which were neither given nor proved. Some of them were certainly with loss of generality. I gave them 0 marks for that question. I’m not sure whether marking in this way is too harsh.
Should students be given partial marks if they gave an incomplete proof by contradiction?