# Math Help - Cardinality of a set

1. ## Cardinality of a set

What is the cardinality of the power set {NULL, a, {NULL}, {{NULL}}}? Why? I believe it is 3.

2. ## Re: Cardinality of a set

Originally Posted by peyton1983
What is the cardinality of the power set {NULL, a, {NULL}, {{NULL}}}? Why? I believe it is 3.
To be very clear, the given set is $\left\{ {\emptyset ,\;a,\;\{ \emptyset \} ,\;\{ \{ \emptyset \} \} } \right\}$.

If that is correct, then that set contains four elements. So what is the carnality of its power set?

3. ## Re: Cardinality of a set

Originally Posted by Plato
To be very clear, the given set is $\left\{ {\emptyset ,\;a,\;\{ \emptyset \} ,\;\{ \{ \emptyset \} \} } \right\}$.

If that is correct, then that set contains four elements.
Unless $a\in\left\{ {\emptyset ,\;\{ \emptyset \} ,\;\{ \{ \emptyset \} \} } \right\}$, in which case it contains three elements.