Question

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

• A. $2^7-2$
• B. $2^7$
• C. $2^7-1$
• D. $2^6-1$

Answer 1

The correct option is C $2^7-1$

If a set contains n elements, then the total number of subsets will be $2^n$, which also includes the subset $\varphi$ and the set itself.

But the set itself will not be considered as a proper subset

Hence, the total number of proper subsets will be $2^n-1$.

In the above case $n=7$.

Hence, the total number of proper subsets will be $2^7-1$