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 (logic)
Famous quotes containing the word laws:
“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)
“The most mighty of nature’s laws is this, that out of Death she brings Life.”
—Herman Melville (1819–1891)
“Our friendships hurry to short and poor conclusions, because we have made them a texture of wine and dreams, instead of the tough fibre of the human heart. The laws of friendship are austere and eternal, of one web with the laws of nature and of morals.”
—Ralph Waldo Emerson (1803–1882)