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Given L= {1,2,4,5,10,20} with divisibility relation.
written 5.2 years ago by | modified 4.0 years ago by |
Verify that $ (L, \le)$ is a distributive but not complimented lattice.
$ \\ $
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written 5.2 years ago by | modified 4.0 years ago by |
Verify that $ (L, \le)$ is a distributive but not complimented lattice.
$ \\ $
written 5.2 years ago by |
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.