The solution says it's not a lattice. I can't figure out why the following is not a lattice...I think I checked the meet (join) of almost every pair.

The solution says it's not a lattice. I can't figure out why the following is not a lattice...I think I checked the meet (join) of almost every pair.

Look at $d$ and $e$: $i$ and $j$ are both minimal (not minimum = least!) upper bounds of $\{d,e\}$, and they’re not comparable, so $d$ and $e$ have no least upper bound.