Choice Function for Set does not imply Choice Function for Union of Set/Mistake

Source Work

 * Chapter $4$: Superinduction, Well Ordering and Choice: Part $\text I$ -- Superinduction and Well Ordering:
 * $\S 4$ Well ordering and choice:
 * Exercise $4.3$
 * Exercise $4.3$

Mistake

 * Show that if there exists a choice function for $S$ then there exists a choice function for $\bigcup S$.

Analysis
Apparently not true.