# Definition of De Morgan's laws in English:

## De Morgan's laws

### plural noun

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 set theory, de Morgan's laws relate the three basic set operations to each other; the union, the intersection, and the complement.’
• ‘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.’

### Origin

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