Power Set/Examples/Set of 3 Elements

Example of Power Set

Let $S = \set {a, b, c}$.

Then the power set of $S$ is:

$\powerset S = \set {\O, \set a, \set b, \set c, \set {a, b}, \set {b, c}, \set {a, c}, S}$

and so has $2^3 = 8$ elements.

Note that while $\set a \in \powerset S$, $a \notin \powerset S$.

Sources

• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 1.8$. Sets of sets: Example $25$