# Set Intersection/Examples/Intersection with Power Set

## Example of Set Intersection

Let $S$ be the set defined as:

$S = \set {1, 2, \set {1, 2} }$

Then the power set of $S$ is:

$\powerset S = \set {\O, \set 1, \set 2, \set {\set {1, 2} }, \set {1, 2}, \set {1, \set {1, 2} }, \set {2, \set {1, 2} }, \set {1, 2, \set {1, 2} } }$

and the intersection of $S$ with $\powerset S$ is:

$S \cap \powerset S = \set {\set {1, 2} }$