Let's call the first set in the question $S_1$ and the second set $S_2$. I'm not necessarily in this example in particular, it's just the first one that came to mind. Obviously, when defining a set that only contains ordered pairs, the first definition is a lot more clear. But if the set contains other elements that aren't ordered pairs, then we have to use an expression similiar to that of $S_2$ to define our set. But what if we are expecting a set that contains both ordered pairs and "singular" elements, which just so happens to have only ordered pairs in it. Is there a way to simplify the set definition so that we end up with a more readable definition, similar to that of $S_1$? Maybe by using rules of predicate logic, or other rules from set theory (which I'm not too familiar with)?
Thank you in advance!