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:
“Nature and Nature’s laws lay hid in night;
God said Let Newton be! and all was light.”
—Alexander Pope (1688–1744)
“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)
“In time of war the laws are silent.”
—Marcus Tullius Cicero (106–43 B.C.)