quick find algorithm - union operation - is it same as union in set theory?

Question

I am unable to correlate union operation in quick find algorithm with general meaning of A U B in set theory.

Book(Algorithms in C++ Robert Sedgewick) tells union operation is "scanning throgh the whole array for each input pair.(line 9 and 10 in code).

Basically we are copying value at node q to all other nodes having same value as node p. Why do we name this operation as UNION?

Code is directly copied from the book.

#include <iostream>
const int N = 10000;
int main() {
int i, p, q, id[N];
for( i = 0; i < N; i++ ) id[i] = i;
while( cin >> p >> q ) {
    int t = id[p];
    if ( t = id[q] ) continue;              //quick find operation
    for ( i = 0; i < N; i++ )               //---> union why?
        if ( id[i] == t) id[i] = id[q];
    cout << " " << p << " " << q << endl;
}
}

Answer 1

The union step in quick find means merging the components with the same id. In a general sense it's kinda like the union of two sets. You can consider two sets, onw with id1 as id of all its components and another as id2. For a great explanation look at this presentation in the quick find section:

http://www.cs.princeton.edu/~rs/AlgsDS07/01UnionFind.pdf