Question $6.$ The following trees represent five sets.

x$3$ x$7$ x$8$ x$12$ x$10$

OO

OO

$??$

OO

$``$

$>>$

OO

OO

x$9$

x$11$

OO

x$1$

x$5$

x$13$

x$4$

x$14$

x$6$

x$2$

Consider the following sequence of union$-$find operations on these sets with UNION BY HEIGHT but NO

path compression.

$1.$ UnionByHeight$($x$2,$x$5)$;

$2.$ FindSet$($x$1)$;

$3.$ FindSet$($x$11)$;

$4.$ UnionByHeight$($x$9,$x$6)$;

$5.$ UnionByHeight$($x$4,$x$6)$;

$6.$ FindSet$($x$4)$;

$7.$ FindSet$($x$9)$;

What element is returned by each of FindSet operations listed above?

Draw the trees representing the final data structure.