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:
“Sweet Cupid’s shafts, like destiny,
Doth causeless good or ill decree.
Desert is born out of his bow,
Reward upon his wing doth go.
What fools are they that have not known
That Love likes no laws but his own!”
—Fulke Greville (1554–1628)
“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)
“I would have these good people to recollect, that the laws of this country hold out to foreigners an offer of all that liberty of the press which Americans enjoy, and that, if this liberty be abridged, by whatever means it may be done, the laws and the constitution, and all together, is a mere cheat; a snare to catch the credulous and enthusiastic of every other nation; a downright imposition on the world.”
—William Cobbett (1762–1835)