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:
“With a generous endowment of motherhood provided by legislation, with all laws against voluntary motherhood and education in its methods repealed, with the feminist ideal of education accepted in home and school, and with all special barriers removed in every field of human activity, there is no reason why woman should not become almost a human thing. It will be time enough then to consider whether she has a soul.”
—Crystal Eastman (1881–1928)
“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.
”
—David Hume (1711–1776)
“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)