Power Set

The number of elements in the power set of a set is equal to $2^n$ , where $n$ stands for the number of $distinct$ elements in the set.

Given S={1, 2, 3, 4}, the cardinality (number of elements) of set S is 4 or n(S)=4

The cardinality of the power set S is denoted as n(p(S))=2^n(S)

Substituting n(S) with 4 to the formula:

n(p(S))=2^4 yields n(p(S))=16