Question

For any set $A$ such that $n\left(A\right)=m,$ match the following:

• A. $2^m$
• B. $2^m-1$
• C. $1$

Answer 1

Given a set $A$ such that $n\left(A\right)=m.$
Power set of $A$ or $P\left(A\right)$ will have all the subsets of $A.$
$\Rightarrow n\left(P\right(A\left)\right)=2^m$

In $P\left(A\right)$ we have only one empty set.
This means number of non - empty subsets of $A=n\left(P\right(A\left)\right)=2^m-1$

Also, a set will have only one Improper Set which is that set itself,
$\Rightarrow$ Number of Improper Subset of $A=1$