Power Set

Definition

$P(S)$, the power set of $S$, is the set of all subsets of $S$

In general, if a set has $n$ elements, the power set has $2^n$ elements

Ex: $S=\{0,1,2\}$

$P(S)=\{\varnothing ,\{0\},\{1\},\{2\},\{0,1\},\{0,2\},\{1,2\},\{0,2,1\}\}$

$|P(S)|=8$

Ex: $A=\varnothing$

$P(A)=\{\varnothing \}$

$|P(A)|=1$

Ex: $B=\{\varnothing \}$

$|B|=1$

$P(B)=\{\varnothing ,\{\varnothing \}\}$

$|P(B)|=2$