Question

$n\left[P\right(A\left)\right]=16$, then $n\left(A\right)=$ ________

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (D)

$4$

If $A$ is a set. Then, $n\left(A\right)$ is called cardinal number of the set A = number of elements in set A.

$P\left(A\right)$ is called power set of $A$. Power set $=P\left(A\right)=$ set of all subsets of set $A$

We know that if number of elements in set $A$ is $n$

$n\left(A\right)=n$

Number of subsets of power set $=2^n$

Given,

$n\left[P\right(A\left)\right]=16$

$2^n=16$

$2^n=2^4$

Therefore, $n=4$