$A$ and $B$ are two non-empty sets and $n\left(A\right)>n\left(B\right)$. The difference of the cardinal numbers of their power sets is $448$. Find the number of elements of $B$.

$A$ and $B$ are non-empty sets, $n\left(A\right)$ and $n\left(B\right)$ are two consecutive odd numbers whose average is $8$ and $n(A\cap B)$ is a prime number. The least possible value of $n(A\cup B)$ is

$A$ and $B$ are non-empty sets, $n\left(A\right)$ and $n\left(B\right)$ are two consecutive odd numbers whose average is $8$ and $n(A\cap B)$ is a prime number. The greatest possible value of $n(A\cup B)$ is 

$A$ and $B$ are any two sets such that $n\left(A\right)>n\left(B\right). P\left(A\right)$ and $P\left(B\right)$ are power sets of $A$ and $B$, respectively, and the difference between cardinal numbers of $P\left(A\right)$ and $P\left(B\right)$ is a three-digit prime number.

The number of elements in set $A$ is

$A$ and $B$ are any two sets such that $n\left(A\right)>n\left(B\right). P\left(A\right)$ and $P\left(B\right)$ are power sets of $A$ and $B$, respectively, and the difference between cardinal numbers of $P\left(A\right)$ and $P\left(B\right)$ is a three-digit prime number.

The number of elements in set $B$ is

$A=\{a, \{b\}, c, \{d, e\left\}\right\}$

Find the number of subsets of $A$ which contain $\left\{b\right\}$ but not $c$