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:
“While I am in favor of the Government promptly enforcing the laws for the present, defending the forts and collecting the revenue, I am not in favor of a war policy with a view to the conquest of any of the slave States; except such as are needed to give us a good boundary. If Maryland attempts to go off, suppress her in order to save the Potomac and the District of Columbia. Cut a piece off of western Virginia and keep Missouri and all the Territories.”
—Rutherford Birchard Hayes (1822–1893)
“The most mighty of nature’s laws is this, that out of Death she brings Life.”
—Herman Melville (1819–1891)
“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)