Question

Match the following sets with cardianality of their power set.

• A. $16$
• B. $1$
• C. $2$

Answer 1

If a set has $m$ elements, then cardinality of their power set equals $2^m.$
Here, For set $A=\{1,2,3,4\}$
$n\left(A\right)=4\Rightarrow n\left(P\right(A\left)\right)=2^4=16$

For set $B=\varnothing$
$n\left(B\right)=0\Rightarrow n\left(P\right(B\left)\right)=2^0=1$

For set $C=\left\{\varnothing \right\}$
$n\left(C\right)=1\Rightarrow n\left(P\right(C\left)\right)=2^1=2$