If you have a set that looks like $S_1 = \{0,1,2,3,4\}$ I understand the cardinality of the set is $5$.
What about if you have a set of sets so
$S_1=\{S_2,S_3,S_4\}$ where,
$S_2=\{1,2,3\}$
$S_3=\{1,2\}$
$S_4=\{1\}$.
For the cardinality of $S_1$ do you count all the elements of the included sets so the answer would be $6$ or do you just count the number in the $S_1$ so it would be $3$.