In other words, complementation is characterized by the complement laws.
2.
The Patriots need a strong cornerback to complement Law.
3.
However the complement laws give the fundamental properties of the somewhat inverse-like unary operation of set complementation.
4.
The first two complement laws above show that if is a non-empty, proper subset of, then } } is a partition of.
5.
The next proposition, which is also self-dual, says that the complement of a set is the only set that satisfies the complement laws.
6.
Note that if the complement laws are weakened to the rule ( A ^ C ) ^ C = A, then this is exactly the algebra of propositional linear logic.
7.
A sufficient subset of the above laws consists of the pairs of associativity, commutativity, and absorption laws, distributivity of'" over ( " ( or the other distributivity law one suffices ), and the two complement laws.
8.
The preceding five pairs of laws & mdash; the commutative, associative, distributive, identity and complement laws & mdash; encompass all of set algebra, in the sense that every valid proposition in the algebra of sets can be derived from them.
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