See these two lines of question:
While there exist sets Si and Sj in the sequence, neither of which is a subset of the other, delete them from the sequence,
ii)If Si∩Sj=∅, then add only the set Si∪Sj to the sequence.
Is not these two lines contradictory?
Say sets are $U=\left \{ 1 \right \},\left \{ 2 \right \},\left \{ 1,2 \right \},\left \{ 1,2,3 \right \}$
Now, here $\left\{ 1 \right \},\left \{ 2 \right \}$ not subset of each other. So, delete both,as a pair?
Remaining $U$ is $\left \{ 1,2 \right \},\left \{ 1,2,3 \right \}$
Now what to add?
I havenot got it.
Another example
Say $U$ is $U=\left \{ 1 \right \},\left \{ 1,2 \right \},\left \{ 1,2,3 \right \},\left \{ 1,2,3,4 \right \},...........\left \{ 1,2,3,4,5,..............\infty \right \}$, the also need to check infinite times. So, then this problem also goes upto infinite.
right??