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:
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.