In propositional logic and boolean algebra, De Morgan's laws are a pair of transformation rules that are both valid rules of inference. The rules allow the expression of conjunctions and disjunctions purely in terms of each other via negation.
The rules can be expressed in English as:
The negation of a conjunction is the disjunction of the negations.
The negation of a disjunction is the conjunction of the negations.
The rules can be expressed in formal language with two propositions P and Q as:
where:
- ¬ is the negation operator (NOT)
- is the conjunction operator (AND)
- is the disjunction operator (OR)
- ⇔ is a metalogical symbol meaning "can be replaced in a logical proof with"
Applications of the rules include simplification of logical expressions in computer programs and digital circuit designs. De Morgan's laws are an example of a more general concept of mathematical duality.
Read more about De Morgan's Laws: Formal Notation, History, Informal Proof, Formal Proof, Extensions
Famous quotes containing the words morgan and/or laws:
“The bread-winner must toil as in the fruitless effort of a troubled dream while the expenditure of an uneducated wife discounts the income in the lack of understanding to discern the broad possibilities of an intelligent economy.”
—Anna Eugenia Morgan (1845–1909)
“Laws can be wrong and laws can be cruel. And the people who live only by the law are both wrong and cruel.”
—Ardel Wray. Mark Robson. Thea (Ellen Drew)