My understanding: The set operations (such as union and intersection) are operations and so functions with a domain and codomain. A function's domain and codomain are always sets. The input to a set operation is either a set or a tuple of sets.
My thoughts: My thoughts about what the domain of a set operation would be (based on the above understanding) has brought me to "the set of all sets". This is clearly wrong.
My Question: What is in fact the domain of a set operation? Am I to instead understand the domain of such an operation to be a class? This would cause me to revise my current understanding of a function to allow the domain and codomain to be classes.