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)
“At present the globe goes with a shattered constitution in its orbit.... No doubt the simple powers of nature, properly directed by man, would make it healthy and a paradise; as the laws of man’s own constitution but wait to be obeyed, to restore him to health and happiness.”
—Henry David Thoreau (1817–1862)
“The chess-board is the world; the pieces are the phenomena of the universe; the rules of the game are what we call the laws of Nature. The player on the other side is hidden from us. We know that his play is always fair, just, and patient. But also we know, to our cost, that he never overlooks a mistake, or makes the smallest allowance for ignorance.”
—Thomas Henry Huxley (1825–1895)