Question

The cardinality of the Power Set of $\{\varphi ,\left\{\varphi \right\},\{\varphi ,\left\{\varphi \right\}\}\}$

• A. Cannot be less than 8.
• B. Is equal to $6$
• C. Is equal to $8$
• D. Can be less than $8$.

Answer 1

Answer: (B), (D)

The correct options are
B Is equal to $6$
D Can be less than $8$.

Let $S=\{\varphi ,\left\{\varphi \right\},\{\varphi ,\left\{\varphi \right\}\}\}$
$P\left(s\right)=$ Power Set of set $S$
$P\left(s\right)=\{\varphi ,\left\{\varphi \right\},\{\varphi ,\left\{\varphi \right\}\},\{\varphi ,\{\varphi ,\left\{\varphi \right\}\}\},\{\left\{\varphi \right\},\{\varphi ,\left\{\varphi \right\}\}\},\{\varphi ,\left\{\varphi \right\},\{\varphi ,\left\{\varphi \right\}\}\}\}$
$n\left(P\right(s\left)\right)=6$.