De Morgan
/də ˈmɔːɡ(ə)n/Logic and Mathematics
noun
1Attributive and in the genitive, especially in De Morgan's law, De Morgan's theorem. Designating two laws of the propositional calculus, (a) that the negation of a conjunction is logically equivalent to the alternation of the negations of the conjoined expressions, and (b) that the negation of an alternation is logically equivalent to the conjunction of the negations of the alternated expressions.
- The laws may be stated symbolically as ∼(p.q) ≡ ∼p ∨ ∼q, and ∼(p ∨ q) ≡ ∼p.∼q, which may be rendered as: (a) if p and q are not jointly true, then p is false or q is false; (b) if neither p nor q is true, then p is false and q is false..
2= De Morgan's theorem.
Origin
Early 20th century; earliest use found in Mind. From the name of Augustus De Morgan, English mathematician, who formulated the laws, although they were known to medieval writers such as William of Ockham (Summa logicae).