List the partitions of the set $S = \{1, 2, 3\}$.

Question

I write the partition sets of set $S=\{1,2,3\}$ as follows:

$\{\{1, 2, 3\}, \{1\}, \{2\}, \{3\}\}$

can someone show me why and how to complete the list?

Answer 1

As the OP said in his comment the answer is the following list of partitions of $S = \{1,2,3\}$:

1. $\left\{ \{1,2,3\} \right\}$ (one set, just $S$ itself )
2. $\left\{ \{1,2\}, \{3\} \right\}$ (two sets, one of two elements , one singleton)
3. $\left\{ \{1,3\}, \{2\} \right\}$
4. $\left\{ \{2,3\}, \{1\} \right\}$
5. $\left\{ \{1\}, \{2\}, \{3\} \right\}$ (all singletons)

and these are all.