S pecial Lattice Definition A lattice L with 0 and 1 is said to be complemented if for every a e L there exists an a' such that aua=1 anda∩a′=0 Sometimes, we can relax the restrictions by defining complement of b relative to a as b∪b=a,b∩b1=0if 6, b1 s a Xam e <P(S), C> is complemented for any nonempty set sSpecial Lattice Definition A lattice L with 0 and 1 is said to be complemented if for every a ∈ L there exists an a 0 such that a ∪ a 0 = 1 and a ∩ a 0 = 0. Sometimes, we can relax the restrictions by defining complement of b relative to a as b ∪ b1 = a, b ∩ b1 = 0 if b, b1 ≤ a. Example < P(S), ⊆> is complemented for any nonempty set S. Yi Li (Fudan University) Discrete Mathematics March 6, 2012 9 / 1