Hypergraph matching

In computational complexity theory, 3-Dimensional Matching is one of the famous [[Karp's 21 NP-complete problems. The problem can be formalized as:

Given $T\subseteq X\times Y\times Z$, and $X,Y,Z$ are disjoint. Does there exist a mathcing Failed to parse (unknown function "\subseteqT"): {\displaystyle M\subseteqT} such that each element of $X,Y,Z$ exists in exactly one set of $M$.