How do I gain intuition on these? I can draw a venn diagram and easily see the relationships being true but I have no fucking clue how to formalize it.
For example: I've been hard stuck on this problem. Idk wtf to do on it. I've tried several ways but they end up being way too long and inefficient. This is supposed to be a baby problem and I'm either clueless or over complicating it. Wtf do I do.

prove the following statements are equivalent:
i) A ? B
ii) A U B = B
iii) A^c U B = Universe

A^c being the complement of A.