Some Additional Laws For Complements
The following proposition states five more important laws of set algebra, involving complements.
PROPOSITION 4: Let A and B be subsets of a universe U, then:
- De Morgan's laws:
-
- double complement or Involution law:
-
- complement laws for the universal set and the empty set:
-
Notice that the double complement law is self-dual.
The next proposition, which is also self-dual, says that the complement of a set is the only set that satisfies the complement laws. In other words, complementation is characterized by the complement laws.
PROPOSITION 5: Let A and B be subsets of a universe U, then:
- uniqueness of complements:
-
- If, and, then
-
Read more about this topic: Algebra Of Sets
Famous quotes containing the words additional and/or laws:
“Don’t you think I’ve had enough excitement for one evening, without the additional thrill of a strange man making love to me?”
—John L. Balderston (1899–1954)
“The main foundations of every state, new states as well as ancient or composite ones, are good laws and good arms ... you cannot have good laws without good arms, and where there are good arms, good laws inevitably follow.”
—Niccolò Machiavelli (1469–1527)