Where x does not already belong to some other set, creates a new set whose only member (and thus representative) is x.
Unites two disjoint, dynamic sets that contain x and y, say $S_x$ and $S_y$, into a new set that is the union of these two sets. Since the sets in the collection must at all times be disjoint, the union(x, y) operation destroys sets $S_x$ and $S_y$, removing them from the collection $S$.
Returns a pointer to the representative of the unique set containing x.
Introduction to Algorithms (Fourth Edition) - Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein (2022)