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Identifying a Distributive Lattice

If it is isomorphic to two standard lattice L1* and  L2*  then the lattice is Not Distributive .
If Complemented Then unique complement should exists .

Identifying a complemented Lattice

Atleast one complement exists for every pair of element . (a,b) are complement to each other if meet and loin of (a,b) are Upper Bound and Lower Bound of lattice .

Is My understanding Correct ??

Q1 ]  POSET [{ 1,2,3,6,12}; / ]
         This POSET is a distributive lattice Eventough complement does not exists for 2,3 .
        IF Complement  exists it should be UNIQE. Atmost one complement for every element
       Is my analysis correct ?
Q2]  POSET [{1,2,3}, <= ]

      What is complemet of 1 , 2 and 3 ? Im not able to find out with above understanding
     

asked in Set Theory & Algebra by Loyal (2.7k points)   | 162 views

2 Answers

+3 votes
1. 1 ----> (2, 3) ---> 6 ----> 12, here complement of 12 is 1. For all other elements complement doesn't exist.

2. 1 ---> 2 ---> 3, here complement of 3 is 1 and complement of 2 doesn't exist.
answered by Veteran (46.5k points)  
Thank you sir
basically if a lattice contains L1* or L2*, it is not distributive. Right ??
0 votes

IN Distributive Lattice atmost one complement of each element should be present.

But In complemented lattice at least one complement of each element should be present.

answered by Loyal (4.9k points)  


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