There are five partitions possible on a set with three elements, say \\( T = {12, 3, 4} \\).

**Example 1.86**.
Let \\( S = {1, 2, 3, 4} \\), \\( T = {12, 3, 4} \\), and \\( g: S \rightarrow T \\) by \\( g(1) = g(2) = 12 , g(3) = 3, \text{ and } g(4) = 4 \\).

Using the same \\( S \\) and \\( g: S \rightarrow T \\) as in Example 1.76,
determine the partition \\( g^\*(c) \\) on \\( S \\) for each of the five partitions \\( c: T \twoheadrightarrow P \\).

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