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:
“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)
“I have no doubt but that the misery of the lower classes will be found to abate whenever the Government assumes a freer aspect and the laws favor a subdivision of Property.”
—James Madison (1751–1836)
“Whenever there are in any country uncultivated lands and unemployed poor, it is clear that the laws of property have been so far extended as to violate natural right. The earth is given as a common stock for man to labor and live on.... The small landowners are the most precious part of a state.”
—Thomas Jefferson (1743–1826)