Two more puzzles connected to [Lecture 3](https://forum.azimuthproject.org/discussion/1812/lecture-3-chapter-1-posets):

**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\\)?

**Puzzle 7.** Why does any set with a reflexive and transitive relation \\(\le\\) yield a category with at most one morphism from any object \\(x\\) to any object \\(y\\)? That is: why are reflexivity and transitivity _enough?_

**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\\)?

**Puzzle 7.** Why does any set with a reflexive and transitive relation \\(\le\\) yield a category with at most one morphism from any object \\(x\\) to any object \\(y\\)? That is: why are reflexivity and transitivity _enough?_