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:
“The process of discovery is very simple. An unwearied and systematic application of known laws to nature causes the unknown to reveal themselves.”
—Henry David Thoreau (1817–1862)
“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)
“The improvements of ages have had but little influence on the essential laws of man’s existence: as our skeletons, probably, are not to be distinguished from those of our ancestors.”
—Henry David Thoreau (1817–1862)