This may be a really stupid question. So say you're doing a proof by contradiction. So you assume the hypothesis and conclusion are true. There are multiple variables involved and I want to consider the case when one only one variable is negative. 1. Are you allowed to do case by case analysis when doing proof by contradiction? In other words, does doing this make sense? 2. If you can use case analysis, must you find a contradiction in each case or is a contradiction in one case good enough? Thanks! I'm very appreciative.