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 can be a true grandeur in any degree of submissiveness, because it springs from loyalty to the laws and to an oath, and not from baseness of soul.”
—Simone Weil (1909–1943)
“It is always a practical difficulty with clubs to regulate the laws of election so as to exclude peremptorily every social nuisance. Nobody wishes bad manners. We must have loyalty and character.”
—Ralph Waldo Emerson (1803–1882)
“Nature and Nature’s laws lay hid in night;
God said Let Newton be! and all was light.”
—Alexander Pope (1688–1744)