self doubt

Question

Is this lattice distributive?

Comments

No , elements have more than one complement.

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which elements have more than 1 complement?

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leftmost and rightmost.

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If you remove the topmost edge  then the graph that  you will get if is present in any graph then that will not be a distributive lattice.

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no, not distributive

As more than one complement present

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is it necessary that if a is complement of then a.b= minimum element of lattice and a+b= maximum element of lattice.

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if there is exatly one or zero complement then lattice is distributive lattice.

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This is a one such type of example where

"every element has at most one complement " but it's not the distributive as it has diamond lattice as sublattice

Answer 1

1. if a lattice have more then one complement then we can directly say it is not distributive lattice.

 2. If there is atleast one element exist who have more then one complement then we can directly say becoz  if  a lattice have exactly 1 or 0 complement then we can say it is distributive lattice .

3. for distributive lattice we check negetivity becoz it is easy for give ans directly.

 

Comments

a,b,c has complements and each have 2 complements

That is why it is not distributive

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Here since L1*is present so we can say it is not distributive lattice

but to check complement ,we have to see that LUB(a,b) = f

and GLB(a,b) = d, d is minimum element of lattice
i am agree with amitqy  , complemented has to be checked if lattice is bounded

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@amitqy did u get what i am saying?