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 laws of God, the laws of man,
He may keep that will and can;
Not I: let God and man decree
Laws for themselves and not for me;”
—A.E. (Alfred Edward)
“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)
“Natural knowledge, seeking to satisfy natural wants, has found the ideas which can alone still spiritual cravings. I say that natural knowledge, in desiring to ascertain the laws of comfort, has been driven to discover those of conduct, and to lay the foundations of a new morality.”
—Thomas Henry Huxley (1825–95)