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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