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:
“Between married persons, the cement of friendship is by the laws supposed so strong as to abolish all division of possessions: and has often, in reality, the force ascribed to it.
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—David Hume (1711–1776)
“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)
“... laws haven’t the slightest interest for me—except in the world of science, in which they are always changing; or in the world of art, in which they are unchanging; or in the world of Being in which they are, for the most part, unknown.”
—Margaret Anderson (1886–1973)