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:
“Let every American, every lover of liberty, every well wisher to his posterity, swear by the blood of the Revolution, never to violate in the least particular, the laws of the country; and never to tolerate their violation by others.”
—Abraham Lincoln (18091865)
“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 (19091943)
“The members of a body-politic call it the state when it is passive, the sovereign when it is active, and a power when they compare it with others of its kind. Collectively they use the title people, and they refer to one another individually as citizens when speaking of their participation in the authority of the sovereign, and as subjects when speaking of their subordination to the laws of the state.”
—Jean-Jacques Rousseau (17121778)