Let \\( \underline{2} = \\\{1, 2\\\} \\) and \\( \underline{3} = \\\{1, 2, 3 \\\} \\).
These are objects in the category **Set**.
Write down all the elements of the set \\( \textbf{Set}( \underline{2}, \underline{3} ) \\); there should be nine.

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The category of sets, denoted **Set**, is defined as follows.

(i) \\( Ob(\textbf{Set}) \\) is the collection of all sets.

(ii) If \\(S\\) and \\(T\\) are sets, then \\( \textbf{Set}(S, T) = \\\{ f : S \rightarrow T | f \text{ is a function } \\\} \\).

(iii) For each set \\(S\\), the identity morphism is the function \\( id_S : S \rightarrow S \\) given by \\( id_S (s) = s \\) for each \\( s \in S \\).

(iv) Given \\( f : S \rightarrow T \\) and \\( g : T \rightarrow U \\), their composite \\(f . g\\) sends \\( s \in S \\) to \\( g( f (s)) \in U \\).