1. The problem statement, all variables and given/known data The real problem is my professor makes anyone who asks a question in class or office hours feel like a total idiot. I Sec.4.4 Problem 18a) https://www.physicsforums.com/showthread.php?t=541479 Could someone comment on whether it would be okay to use part a) in part b)? 2. Relevant equations Above we proved, for all x element of A, x is an upper bound of B1 iff x is an upper bound of B2. Can we use this in part b)? Although b) is talking about a maximal element instead of an upper bound. I think the only difference is that maximal element is part of the subset. 3. The attempt at a solution Contra positive. Assume B1 has a maximal element b1. This means that there does not exist an x є B1(b1Rx Λ b1 ≠ x). By part a), we know that b1 is also the maximal element of B2. Therefore, b1 є (B1 and B2). Therefore, B1 and B2 are not disjoint.