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:
“Sadder than destitution, sadder than a beggar is the man who eats alone in public. Nothing more contradicts the laws of man or beast, for animals always do each other the honor of sharing or disputing each other’s food.”
—Jean Baudrillard (b. 1929)
“The laws of God, the laws of man,
He may keep that will and can;
Not I: let God and man decree
Laws for themselves and not for me;”
—A.E. (Alfred Edward)
“Kings have many ears and many eyes.... They have ears that listen a hundred miles from them; they have eyes that espy out more things than men would think. Wherefore, it is wisdom for subjects not only to keep their princes’ laws and ordinances in the face of the world but also privily ... for conscience sake.”
—Desiderius Erasmus (c. 1466–1536)