If $A=\left\{1, 2, 3, 4\dots \dots n\right\}$ and $B\subseteq A; C\subseteq A,$ then find the number of ways of selecting
$\left(i\right)$ Sets $B$ and $C$
$\left(ii\right)$ Order pair of $B$ and $C$ such that $B\cap C=\varphi$
$\left(iii\right)$ Unordered pair of $B$ and $C$ such that $B\cap C=\varphi$
$\left(iv\right)$ Ordered pair of $B$ and $C$ such that $B\cup C=A$ and $B\cap C=\varphi$
$\left(v\right)$ Unordered pair of $B$ and $C$ such that $B\cup C=A, B\cap C=\varphi$
$\left(vi\right)$ Ordered pair of $B$ and $C$ such that $B\cap C$ is a singleton