Distributive lattice
![Young's lattice](/Images/godic/202501/14/Young's_lattice.svg3949.png")
![Distributive lattice which contains N5 (solid lines, left) and M3 (right) as subset, but not as sublattice, respectively](/Images/godic/202501/14/Non-dstrbtive_lattices-warning3949.png")
![Free distributive lattices on zero, one, two, and three generators. The elements labeled](/Images/godic/202501/14/Monotone_Boolean_functions.svg3949.png")
In mathematics, a distributive lattice is a lattice in which the operations of join and meet distribute over each other. The prototypical examples of such structures are collections of sets for which the lattice operations can be given by set union and intersection. Indeed, these lattices of sets describe the scenery completely: every distributive lattice is – up to isomorphism – given as such a lattice of sets.