Given the Hasse diagram tell if the structure is a lattice

Let’s consider the following Hasse diagram:

$M_5$

I need to tell whether this is a lattice. By lattice definition I can prove the above shown structure Mto be a lattice if and only if yM∀x,y ∈M5, {x,y} has supremum and infimum in M5. Putting all such subsets in a table, not mentioning those subset where x=:

So the M5 is a lattice.

If you are a beginner we would recommend you to watch this video to learn lattices Topic in more effective way.

You can Also Learn More about Hasse Diagram from Here.

Leave a Reply

Your email address will not be published. Required fields are marked *