Question

A finite set $S$ is given by $S=\{x:x\in N:x\le 15\}.$ Find the cardinality of its power set.

• A. 32952
• B. 16384
• C. 32768
• D. 16476

Answer 1

The correct option is C 32768

$S$ is given by $S=\{x:x\in N:x\le 15\}$
$S=\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15\}$
$\therefore n\left(S\right)=15$
The power set is set of all the possible subsets of $S.$
Number of elements in power set $=$ Total number of subsets
So, cardinality of power set $S=2^{15}=32768$