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 womanwhether you win the Nobel Prize or merely get tenure at the cost of denying your sistersis 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)
“However great a mans fear of life, suicide remains the courageous act, the clear- headed act of a mathematician. The suicide has judged by the laws of chanceso 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 (19041991)
“Nature and natures laws lay hid in the night. God said, Let Newton be! and all was light!”
—Alexander Pope (16881744)