Boolean lattice
From AoPSWiki
Given any set 
, the boolean lattice 
is a partially ordered set whose elements are those of 
, the power set of , ordered by inclusion (
).
When has a finite number of elements (say 
), the boolean lattice associated with is usually denoted 
. Thus, the set 
is associated with the boolean lattice 
with elements 
and 
, among which 
is smaller than all others, is larger than all others, and the other six elements satisfy the relations 
, 
, 
and no others.
The Hasse diagram for is given below:
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Every boolean lattice is a distributive lattice, and the poset operations meet and join correspond to the set operations union and intersection.
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