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I'm supposed to find an 8-element complete lattice which does not form a Boolean algebra.
Sadly, anything I can think of is either not a complete lattice or it is a Boolean algebra.

I think that what i need is a lattice in this shape:
enter image description here

Since it would not be distributive. But I still can't get my head around one thing - since a lattice is basically an ordering on a given set, I have to provide the whole set and a measure by which it is ordered. And I can't think of any set and ordering that would form this lattice.

Maybe I'm totally mistaken, honestly I don't understant it much. Any help is welcomed.

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    There are a few references above to an "8-element complete lattice." The adjective "complete" is redundant and should be left out to avoid confusion. All finite lattices are complete.2012-03-19

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