Whether it is a lattice? Why or Why not?

152 Views Asked by Bumbble Comm At 01 Apr 2026 - 10:23

enter image description here Whether it is a lattice? Why or Why not?

In this diagram every pair has GLB and LUB.

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Bumbble Comm On 02 Oct 2013 - 3:09 BEST ANSWER

It is not a lattice, because the pair $\{d,e\}$ has no least upper bound; it has upper bounds $a,b,c$ but no least upper bound.

Likewise, the pair $\{b,c\}$ has no greatest lower bound.