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:
“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)
“Let every American, every lover of liberty, every well wisher to his posterity, swear by the blood of the Revolution, never to violate in the least particular, the laws of the country; and never to tolerate their violation by others.”
—Abraham Lincoln (1809–1865)
“... I want to live and be happy. I believe that we cannot be one or the other by pushing the absurd to all its consequences. I am like everyone. To feel liberated, I sometimes wish death on my loved ones, I covet the wives forbidden to me by the laws of family and friendship. To be logical, I should then kill or possess. But I judge that these vague ideas are unimportant. I everyone tried to put them to reality, we could neither live nor be happy.”
—Albert Camus (1913–1960)