Cardinality/Examples/Powerset of Arbitrary Set

Example of Cardinality
Let:
 * $S_4 = \set {X \in \powerset {S_2}: \card X = 3}$

where $S_2 = \set {x \in \Z: 0 < x < 6}$.

The cardinality of $S_4$ is given by:
 * $\card {S_4} = 10$

Proof
By Cardinality of $S_2$, we have that:
 * $\card {S_2} = 5$

Then:

Hence the result by definition of cardinality.