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:
“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)
“It is a power stronger than will.... Could a stone escape from the laws of gravity? Impossible. Impossible, for evil to form an alliance with good.”
—Isidore Ducasse, Comte de Lautréamont (1846–1870)
“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)