**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.