Does this "set intersection" problem have a different name? I've been back and forth about this one. I have the following theoretical homework problem, which describes the SET-INTERSECTION problem. In my homework, it's presented as being NP-complete.



Does this problem have a more common name in general Computer Science nomenclature? I'm trying to wrap my head around the definition itself -- and I can't find any resources that refer to the "set intersection problem" with similar parameters to this except in this pdf. It seems similar to the unit intersection problem described in a math stackexchange post. I also (naively?) think that it might be the set cover problem.

My actual intent is to understand what the problem describes -- so I'm looking for alternate names and resources that lead in the right direction. I'm not asking for any specific help in proving properties of it -- just understanding what it describes.
To the best of my knowledge, there is no other name for this.