Question

For a set $K,\text{if}n\left(K\right)=m;$ then the number of proper subsets of $K=$

• A. $2^m-1$
• B. $2^{m-1}$
• C. $2^m$

Answer 1

The correct option is A $2^m-1$

Given a set $K$ such that $n\left(K\right)=m$
Now improper set of any set is that set itself.
Since $2^m$ is the total number of subsets of any sets.
$\therefore$ Total number of proper subsets of a set $=2^m-1.$