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:
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- double complement or Involution law:
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- complement laws for the universal set and the empty set:
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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:
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- If, and, then
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Read more about this topic: Algebra Of Sets
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