What is the cardinality of the power set {NULL, a, {NULL}, {{NULL}}}? Why? I believe it is 3.
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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 $\displaystyle \left\{ {\emptyset ,\;a,\;\{ \emptyset \} ,\;\{ \{ \emptyset \} \} } \right\}$. If that is correct, then that set contains four elements. So what is the carnality of its power set?
Originally Posted by Plato To be very clear, the given set is $\displaystyle \left\{ {\emptyset ,\;a,\;\{ \emptyset \} ,\;\{ \{ \emptyset \} \} } \right\}$. If that is correct, then that set contains four elements. Unless $\displaystyle a\in\left\{ {\emptyset ,\;\{ \emptyset \} ,\;\{ \{ \emptyset \} \} } \right\}$, in which case it contains three elements.
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