I would like to try to solve the following problems.
Problem from the Oriented Matroids book by Bjorner, Las Vergnas, Sturmfels, White, and Ziegler. It is problem 3.9 on page 152.
Attempt
Now quite sure what to do from there with part (a). If someone knows how to prove at least part (a), could you show me the proof? I am having a LOT of trouble understanding oriented matroid theory. Thank you very much. I will highly rate for your help.
How can you prove that $\text{conv} : 2^E\rightarrow 2^E$ is a closure operator?