I am interested in the following simple problem: Let $X$ be a set and $X_1\cup X_2\cup\cdots\cup X_k$ be a finite partition of $X$. Given $x\in X$, find the subset $X_i$ for which $x\in X_i$. I am mostly interested in some general background on this problem. I'm stuck because I do not know of a canonical "name" for this problem.
Does this problem have a name, or is there a closely related problem that might generate some useful hits?