Total Number of Set Partitions/Examples/4/Illustration

Example of Total Number of Set Partitions
Let a set $S$ of cardinality $4$ be exemplified by $S = \set {a, b, c, d}$.

Then the partitions of $S$ are:


 * $\set {a, b, c, d}$


 * $\set {a \mid b, c, d}$
 * $\set {b \mid a, c, d}$
 * $\set {c \mid a, b, d}$
 * $\set {d \mid a, b, c}$


 * $\set {a, b \mid c, d}$
 * $\set {a, c \mid b, d}$
 * $\set {a, d \mid b, c}$


 * $\set {a \mid b \mid c, d}$
 * $\set {a \mid c \mid b, d}$
 * $\set {a \mid d \mid b, c}$


 * $\set {b \mid c \mid a, d}$
 * $\set {b \mid d \mid a, c}$
 * $\set {c \mid d \mid a, b}$


 * $\set {a \mid b \mid c \mid d}$