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:
“When I turned into a parent, I experienced a real and total personality change that slowly shifted back to the “normal” me, yet has not completely vanished. I believe the two levels are now superimposed, with an additional sprinkling of mortality intimations.”
—Sonia Taitz (20th century)
“The new always happens against the overwhelming odds of statistical laws and their probability, which for all practical, everyday purposes amounts to certainty; the new therefore always appears in the guise of a miracle.”
—Hannah Arendt (1906–1975)