De Morgan's laws

De Morgan's laws state that the complement of a meet is the join of the complements, and the complement of a join is the meet of the complements.

Lattice: A partially ordered set in which every pair of elements has a greatest lower bound and a least upper bound. The laws describe how complementation interacts with a lattice's meet and join.
Propositional calculus: A formal system for reasoning with propositions connected by logical operators. Negating a conjunction or disjunction applies the laws directly.
Truth table: A table listing the output of a logical expression for every possible assignment of its inputs. Truth tables verify both identities for propositional logic.
Distributive lattice: A lattice in which meet distributes over join and join distributes over meet. Boolean algebras add complementation to this structure, where the familiar identities hold.
Augustus De Morgan: A British mathematician and logician who helped develop symbolic logic in the nineteenth century. The laws bear his name and appeared in his work on formal logic.
Meet (order theory): The greatest lower bound of two elements in a partially ordered set. It is the operation whose complement becomes a join of complements.
Set theory: The mathematical study of sets and their relationships. Set intersection, union, and relative complement realize the lattice identities.
Order duality: The principle that reverses an order relation while exchanging corresponding upper- and lower-bound operations. Complementation reverses order, exchanging meet and join in the laws.
Orthocomplemented lattice: A bounded lattice with an order-reversing involution satisfying specified complement conditions. Its generalized De Morgan identities need not imply Boolean distributivity.
George Boole: A British mathematician whose algebraic methods helped establish modern symbolic logic. Boole's algebra gave the identities a systematic algebraic setting.

Linked from 1 page