meetdistributesoverjoin
Meetdistributesoverjoin, in lattice theory, refers to the distributive law where the meet operation distributes over the join operation. In a lattice L with binary operations meet (∧) and join (∨), the property states that for all elements a, b, and c in L, a ∧ (b ∨ c) = (a ∧ b) ∨ (a ∧ c). This law is one half of the standard distributivity conditions that define a distributive lattice.
A lattice is called distributive when both distributive laws hold: a ∧ (b ∨ c) = (a ∧ b) ∨ (a
Examples where the law holds include Boolean algebras and the lattice of subsets of a set under
In practice, meet distributing over join is fundamental to simplifying expressions in logic, set theory, and