0
5.8kviews
Given L= {1,2,4,5,10,20} with divisibility relation.

Verify that $ (L, \le)$ is a distributive but not complimented lattice.

$ \\ $

1 Answer
0
798views

L = {1,2,4,5,10,20}

$ (L, \le )$

the hasse diagram for L is shown in figure.

enter image description here

Element 7 2 4 5 10 20
Complement 20 No Complement 10 No Complement 4 1

This is a distributive lattice as either every element has one complement or no complement.

This is not a complimented lattice as element 2 and element 5 does not have compliment.

Please log in to add an answer.