Subsets and Power Set

In interval notation$(a,b)=x|a<x<b,(a,b)$represents

If $\mathrm{A}=\{1, 2, 3, 4, 5, 6, 7\}$, then the number of proper subsets of $\mathrm{A}$ is

Find the length of interval $\left(8,32\right)$.

Find the length of interval $\left(4,26\right)$.

Find the length of interval $\left(2,14\right)$.

Find the length of interval $\left(5,16\right)$.

Find the length of interval $\left(3,21\right)$.

Write a superset of the following set.

$A=\left\{7,8\right\}$

Write a superset of the following set.

$A=\left\{6,7,8\right\}$

Write a superset of the following set.

$A=\left\{2,3\right\}$

Write a superset of the following set.

$A=\left\{2,3,4\right\}$

Write a superset of the following set.

$A=\left\{2,3,4,5\right\}$

Match the List $\mathrm{I}$ and List $\mathrm{II}$ and select the correct answer using code:

Find the number of subsets for the set given below.

$M=\left\{x\in Z, {100}^{\left(x^2-x-2\right)}=1\right\}$

If $A$ and $B$ be two finite sets such that the total number of subsets of $A$ is $960$ more than the total number of subsets of $B,$ then $n\left(A\right)-n\left(B\right)$ (where $n\left(X\right)$ denotes the number of elements in set $X$) is equal to

A relation on the set $\text{A}=\left\{\text{x }\text{: }\left|\text{x}\right|<3\text{, }\text{x }\in \text{Z}\right\}\text{,}$ where $z$ is the set of integers is defined by $\text{R}=\left\{\left(\text{x}\text{, }\text{y}\right)\text{ :}\text{ y}=\left|\text{x}\right|\text{, }\text{x}\ne -1\right\}$. Find total elements in the power set of $R$.

If $n\left(A\right)=3,n\left(B\right)=6$ and $A\subseteq B$ . Then the number of elements in $A\cup B$ is equal to

If $A$ is an empty set and $P\left(A\right)$ denotes power set of $A$, then number of elements in $P\left(P\left(P\left(P\left(P\left(A\right)\right)\right)\right)\right)$ is

If a set contains $p$ elements and another set contains $q$ elements. If $96$ is the difference between the number of subsets of both sets, then find $\left(p,q\right)$.

Find the power sets $\mathcal{P}\left(A\right)$ and $\mathcal{P}\left(B\right)$ where $A=\{a, b, \{c, d\left\}\right\}$ and $B=\left\{\right\{a\}, \{b\left\}\right\}$