I am currently working on proving these statements and , by means of subsets (I've heard that is is also referred to as, "proof by double inclusion."). I am having trouble with these sort of problems, so I'd certainly appreciate the help.
Here is my work:
Suppose that ; for to be in the set, can't be in . This means that ; however, by this fact, can be in , , or . Thus, when , is also in , meaning that
I have not commenced the second part, yet, because I feel as though there is something wrong with this, and I feel like I might have left out steps and explanations.