# de Morgan's laws

Syllabification: de Mor·gan's laws
Pronunciation: /də ˈmôrɡənz ˌlôz /
Mathematics

## Definition of de Morgan's laws in English:

Two laws in Boolean algebra and set theory that state that AND and OR, or union and intersection, are dual. They are used to simplify the design of electronic circuits.
• The laws can be expressed in Boolean logic as: NOT (a AND b) = NOT a OR NOT b; NOT (a OR b) = NOT a AND NOT b
Example sentences
• In logic, De Morgan's laws (or De Morgan's theorem), named for nineteenth century logician and mathematician Augustus De Morgan, are two powerful rules of Boolean algebra and set theory.
• This completes the proof of the first of De Morgan's laws; the second is obtained by similar reasoning.
• In set theory, de Morgan's laws relate the three basic set operations to each other; the union, the intersection, and the complement.

### Origin

early 20th century: named after Augustus de Morgan (1806–71), English mathematician, but already known (by logicians) as principles in the Middle Ages.

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Pronunciation: ˈkəmbərsəm