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:
“So far as laws and institutions avail, men should have equality of opportunity for happiness; that is, of education, wealth, power. These make happiness secure. An equal diffusion of happiness so far as laws and institutions avail.”
—Rutherford Birchard Hayes (1822–1893)
“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)
“It is clear that in a monarchy, where he who commands the exceution of the laws generally thinks himself above them, there is less need of virtue than in a popular government, where the person entrusted with the execution of the laws is sensible of his being subject to their direction.”
—Charles Louis de Secondat Montesquieu (1689–1755)