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 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)
“However great a man’s fear of life, suicide remains the courageous act, the clear- headed act of a mathematician. The suicide has judged by the laws of chance—so many odds against one that to live will be more miserable than to die. His sense of mathematics is greater than his sense of survival.”
—Graham Greene (1904–1991)
“It is always a practical difficulty with clubs to regulate the laws of election so as to exclude peremptorily every social nuisance. Nobody wishes bad manners. We must have loyalty and character.”
—Ralph Waldo Emerson (1803–1882)