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

written 6.9 years ago by teamques10 ★ 70k

modified 5.7 years ago by parviagrawal100 • 0

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

$ \\ $

engineering mathematics

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written 6.9 years ago by teamques10 ★ 70k

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

$ (L, \le )$

the hasse diagram for L is shown in figure.

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.

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