Given a set $B = \{ \{1,4\}, a, b, \{\{3, 4\}\}, \{\emptyset\} \}$,
find the cardinality of $B$
my answer is $5$,
and it is from $\{1,4\}, a, b, \{\{3, 4\}\}, \{\emptyset\}$, which is $5$ elements
However I'm unsure if that is the correct answer because $\{\{3, 4\}\}$ has a set $\{3,4\}$ within a set.
The resource I found on-line says that:
Given $F = \{ \emptyset, \{\emptyset\}, \{\{\emptyset\}\} \}$,
the cardinality of $F = 3$,
where $\emptyset$ is one, $\{\emptyset\}$ is one, and $\{\{\emptyset\}\}$ is another one.
Therefore I figure $\{\{3,4\}\}$ should also be counted as one cardinal as well.
Please give me some advice, thanks in advance.
Best Answer
You are correct.
The only way you could be wrong (in which case this would be a trick question) is if $a$ or $b$ was equal to one of the other elements of the set, e.g. $a = b$ or $a = \{\{3,4\}\}$.