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:
“To become a token woman—whether you win the Nobel Prize or merely get tenure at the cost of denying your sisters—is to become something less than a man ... since men are loyal at least to their own world-view, their laws of brotherhood and self-interest.”
—Adrienne Rich (b. 1929)
“Nature and nature’s laws lay hid in the night. God said, Let Newton be! and all was light!”
—Alexander Pope (1688–1744)
“Whenever there are in any country uncultivated lands and unemployed poor, it is clear that the laws of property have been so far extended as to violate natural right. The earth is given as a common stock for man to labor and live on.... The small landowners are the most precious part of a state.”
—Thomas Jefferson (1743–1826)