 ##  [De Morgan's Laws](/de-morgans-laws) 

  ##  [De Morgan's Laws](https://natural.quantumdictionary.io/de-morgans-laws-0) 

  
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**Natural &amp; Formal Sciences Dictionary**

 
Definition

Rules in propositional logic and set theory stating that the negation of a conjunction equals the disjunction of the negations, and the negation of a disjunction equals the conjunction of the negations (¬(A∧B) ⇔ ¬A∨¬B and ¬(A∨B) ⇔ ¬A∧¬B), with corresponding set complement analogues.

 
 ##  [De Morgan's Laws](https://mathlogic.quantumdictionary.io/de-morgans-laws-1) 

  
 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

The pair of logical equivalences that relate negation with conjunction and disjunction: ¬(A ∧ B) is equivalent to (¬A) ∨ (¬B), and ¬(A ∨ B) is equivalent to (¬A) ∧ (¬B) in classical logic and Boolean algebra.

 
 ##  [De Morgan's Laws](https://algebra.quantumdictionary.io/de-morgans-laws-2) 

  
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- Pure Mathematics -

**Algebra Dictionary**

 
Definition

Two algebraic rules that describe how complementation (logical negation or set complement) distributes over the binary operations of union and intersection (or OR and AND): the complement of a union equals the intersection of the complements, and the complement of an intersection equals the union of the complements.