* Choose two sets X and Y with at least three elements each.

* Choose a surjective, non-identity function \\( f : X \rightarrow Y \\) between them.

* Write down two different partitions \\(P\\) and \\(Q\\) of \\(Y\\), and then find \\( f^\*(P) \\) and \\( f^\*(Q) \\).

* Choose a surjective, non-identity function \\( f : X \rightarrow Y \\) between them.

* Write down two different partitions \\(P\\) and \\(Q\\) of \\(Y\\), and then find \\( f^\*(P) \\) and \\( f^\*(Q) \\).