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- De_Morgan_algebra abstract "In mathematics, a De Morgan algebra (named after Augustus De Morgan, a British mathematician and logician) is a structure A = (A, ∨, ∧, 0, 1, ¬) such that: (A, ∨, ∧, 0, 1) is a bounded distributive lattice, and ¬ is a De Morgan involution: ¬(x ∧ y) = ¬x ∨ ¬y and ¬¬x = x. (i.e. an involution that additionally satisfies De Morgan's laws)In a De Morgan algebra: ¬x ∨ x = 1 (law of the excluded middle), and ¬x ∧ x = 0 (law of noncontradiction)do not always hold (when they do, the algebra becomes a Boolean algebra).Remark: It follows that ¬( x∨y) = ¬x∧¬y, ¬1 = 0 and ¬0 = 1 (e.g. ¬1 = ¬1∨0 = ¬1∨¬¬0 = ¬(1∧¬0) = ¬¬0 = 0). Thus ¬ is a dual automorphism.De Morgan algebras are important for the study of the mathematical aspects of fuzzy logic. The standard fuzzy algebra F = ([0, 1], max(x, y), min(x, y), 0, 1, 1 − x) is an example of a De Morgan algebra where the laws of excluded middle and noncontradiction do not hold.".
- De_Morgan_algebra wikiPageID "8495580".
- De_Morgan_algebra wikiPageRevisionID "596925857".
- De_Morgan_algebra hasPhotoCollection De_Morgan_algebra.
- De_Morgan_algebra subject Category:Algebra.
- De_Morgan_algebra subject Category:Algebraic_logic.
- De_Morgan_algebra subject Category:Lattice_theory.
- De_Morgan_algebra comment "In mathematics, a De Morgan algebra (named after Augustus De Morgan, a British mathematician and logician) is a structure A = (A, ∨, ∧, 0, 1, ¬) such that: (A, ∨, ∧, 0, 1) is a bounded distributive lattice, and ¬ is a De Morgan involution: ¬(x ∧ y) = ¬x ∨ ¬y and ¬¬x = x. (i.e.".
- De_Morgan_algebra label "De Morgan algebra".
- De_Morgan_algebra sameAs m.0275hzt.
- De_Morgan_algebra sameAs Q5244640.
- De_Morgan_algebra sameAs Q5244640.
- De_Morgan_algebra wasDerivedFrom De_Morgan_algebra?oldid=596925857.
- De_Morgan_algebra isPrimaryTopicOf De_Morgan_algebra.