**Puzzle 66.** Let us pick the unit, \\(I\\), to be any element of the preorder \\(P\\), and let the binary operation always return the unit, that is, \\(x \otimes y = I\\) for all \\(x, y \in P\\); then:

1. \\( (P, \otimes, I) \\) is a monoid.

2. \\(x \otimes y \le x' \otimes y'\\) holds for all \\(x, y, x', y' \in P\\), because of reflexivity on \\(I\\).

So, it seems that any poset can be turned into a monoidal poset.

**Edit:** As pointed out below by Jonathan, my answer is flawed – this happened because I was sloppy and I skipped some parts of the proof.

1. \\( (P, \otimes, I) \\) is a monoid.

2. \\(x \otimes y \le x' \otimes y'\\) holds for all \\(x, y, x', y' \in P\\), because of reflexivity on \\(I\\).

So, it seems that any poset can be turned into a monoidal poset.

**Edit:** As pointed out below by Jonathan, my answer is flawed – this happened because I was sloppy and I skipped some parts of the proof.