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:
“To become a token woman—whether you win the Nobel Prize or merely get tenure at the cost of denying your sisters—is to become something less than a man ... since men are loyal at least to their own world-view, their laws of brotherhood and self-interest.”
—Adrienne Rich (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)
“Thus far women have been the mere echoes of men. Our laws and constitutions, our creeds and codes, and the customs of social life are all of masculine origin. The true woman is as yet a dream of the future. A just government, a humane religion, a pure social life await her coming.”
—Elizabeth Cady Stanton (1815–1902)