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:
“All over this land women have no political existence. Laws pass over our heads that we can not unmake. Our property is taken from us without our consent. The babes we bear in anguish and carry in our arms are not ours.”
—Lucy Stone (1818–1893)
“The members of a body-politic call it “the state” when it is passive, “the sovereign” when it is active, and a “power” when they compare it with others of its kind. Collectively they use the title “people,” and they refer to one another individually as “citizens” when speaking of their participation in the authority of the sovereign, and as “subjects” when speaking of their subordination to the laws of the state.”
—Jean-Jacques Rousseau (1712–1778)
“The counting-room maxims liberally expounded are laws of the Universe. The merchant’s economy is a coarse symbol of the soul’s economy. It is, to spend for power, and not for pleasure.”
—Ralph Waldo Emerson (1803–1882)