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Why the following Hasse Diagram is not a lattice ...?

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It is a lattice.. but not a distributive lattice..
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@Amsar_Sokt Sir , Which elements have multiple complements ?
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Here,  a has two complements  - b & c

becz,   (a ∨ b = 1)   &   (a ∧ b ) = 0  =>  b is compliment of a & vice versa..

          same applies for a & c..

a

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Thx :)
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1 Answer

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definition of lattice - every pair of elements should have unique least upper bound and greatest lower bound.

here this hasse diagram has unique LUB and GLB . hence this hasse diagram is lattice. but not distributive lattice as a have more than one complement i.e. b and c .
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