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:
“If we are related, we shall meet. It was a tradition of the ancient world, that no metamorphosis could hide a god from a god; and there is a Greek verse which runs, “The Gods are to each other not unknown.” Friends also follow the laws of divine necessity; they gravitate to each other, and cannot otherwise.”
—Ralph Waldo Emerson (1803–1882)
“Herein is the explanation of the analogies, which exist in all the arts. They are the re-appearance of one mind, working in many materials to many temporary ends. Raphael paints wisdom, Handel sings it, Phidias carves it, Shakspeare writes it, Wren builds it, Columbus sails it, Luther preaches it, Washington arms it, Watt mechanizes it. Painting was called “silent poetry,” and poetry “speaking painting.” The laws of each art are convertible into the laws of every other.”
—Ralph Waldo Emerson (1803–1882)
“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 (1809–1865)