**Puzzle 6.** How do reflexivity and transitivity of \\(\le\\) follow from the rules of a category, if we have a category with at most one morphism from any object \\(x\\) to any object \\(y\\), and we write \\(x \le y\\) when there exists a morphism from \\(x\\) to \\(y\\)?

Answer. Reflexivity follows from the existence of identity morphisms in a category. Transitivity follows from the fact that given morphisms f: A -> B, and g: B -> C, the composite morphism taking A -> C is provided by the category.