S pecial Lattice Definition A lattice L is distributive if for any a, b, c E L such that o an(bUc=(anb)u(anc aU(b∩c)=(a∪b)∩(aUc If a lattice is not distributive. we call it non-distributive Xam le <P(S), C> is distributive for any nonempty set sSpecial Lattice Definition A lattice L is distributive if for any a, b, c ∈ L such that: 1 a ∩ (b ∪ c) = (a ∩ b) ∪ (a ∩ c). 2 a ∪ (b ∩ c) = (a ∪ b) ∩ (a ∪ c). If a lattice is not distributive, we call it non-distributive. Example < P(S), ⊆> is distributive for any nonempty set S. Yi Li (Fudan University) Discrete Mathematics March 6, 2012 11 / 1