Laws
A law of Boolean algebra is an equation such as x∨(y∨z) = (x∨y)∨z between two Boolean terms, where a Boolean term is defined as an expression built up from variables and the constants 0 and 1 using the operations ∧, ∨, and ¬. The concept can be extended to terms involving other Boolean operations such as ⊕, →, and ≡, but such extensions are unnecessary for the purposes to which the laws are put. Such purposes include the definition of a Boolean algebra as any model of the Boolean laws, and as a means for deriving new laws from old as in the derivation of x∨(y∧z) = x∨(z∧y) from y∧z = z∧y as treated in the section on axiomatization.
Read more about this topic: Boolean Algebra
Famous quotes containing the word laws:
“There is something servile in the habit of seeking after a law which we may obey. We may study the laws of matter at and for our convenience, but a successful life knows no law.”
—Henry David Thoreau (1817–1862)
“Sadder than destitution, sadder than a beggar is the man who eats alone in public. Nothing more contradicts the laws of man or beast, for animals always do each other the honor of sharing or disputing each other’s food.”
—Jean Baudrillard (b. 1929)
“Surely the fates are forever kind, though Nature’s laws are more immutable than any despot’s, yet to man’s daily life they rarely seem rigid, but permit him to relax with license in summer weather. He is not harshly reminded of the things he may not do.”
—Henry David Thoreau (1817–1862)