Let \$$\mathcal{C}\$$ be an arbitrary category and let \$$\mathcal{P}\$$ be a preorder, thought of as a category.
Consider the following statements:

1. For any two functors \$$F, G : \mathcal{C} \rightarrow \mathcal{P}\$$, there is at most one natural transformation
\$$F \rightarrow G\$$.
2. For any two functors \$$F, G : \mathcal{P} \rightarrow \mathcal{C}\$$, there is at most one natural transformation
\$$F \rightarrow G\$$.

For each, if it is true, say why; if it is false, give a counterexample.

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