One of the mysteries of the English language finally explained.
Mathematics
Two laws in Boolean algebra and set theory which 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
- ‘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.’
- ‘de Morgan's laws are named after the Indian-born British mathematician and logician Augustus De Morgan (1806-1871).’
- ‘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.