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