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 word laws:
“The Laws of Nature are just, but terrible. There is no weak mercy in them. Cause and consequence are inseparable and inevitable. The elements have no forbearance. The fire burns, the water drowns, the air consumes, the earth buries. And perhaps it would be well for our race if the punishment of crimes against the Laws of Man were as inevitable as the punishment of crimes against the Laws of Nature—were Man as unerring in his judgments as Nature.”
—Henry Wadsworth Longfellow (1807–1882)