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Let $S=\{1,2,3\}$. Write all the possible partitions of $S$.
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Remember that a partition of $S$ is a collection of nonempty sets that are disjoint and their union is
$S$. There are 5 possible partitions for $S=\{1,2,3\}$ :

1. $\{1\},\{2\},\{3\}$;
2. $\{1,2\},\{3\}$;
3. $\{1,3\},\{2\}$
4. $\{2,3\},\{1\} ;$
5. $\{1,2,3\}$.
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