The Answer should be $E$.
Let's say my Universe consist of only two elements $\{1,2\}$ and I define two subsets $s_1 = \{1\}, s_2 = \{1,2\}.$ And Sequence $S = s_1s_2 = \{1\}\{1,2\}$.
Initially - $\{1\}\{1,2\}$
$Step \ 1$ - $\{1,2\}\{1\}$
$S_1 \cap S_2$ is not null so we delete these two sets and add $S_1 \cup S_2$ which will be = $\{1,2\}$ and there intersection which will be = $\{1\}$. Now we got the same sets in the sequence again. If we again do the same procedure then again we get the same set. So only Option E matches.
$Step \ 2$ - $\{1\}\{1,2\}$
$Step \ 3$ - $\{1,2\}\{1\}$
$\vdots$
A is false likewise B because the size of smallest and largest set is constant in every step. Infact smallest set and largest set can change in any step.
Note that as soon as we find 2 consecutive sets in the sequence such that one is the subset of other, they will get repeated again and again and the process never terminates.
So C and D are false.