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 Stage but echoes back the publick Voice.
The Drama’s Laws the Drama’s Patrons give,
For we that live to please, must please to live.”
—Samuel Johnson (1709–1784)
“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)
“The putting into force of laws which shall secure the conservation of our resources, as far as they may be within the jurisdiction of the Federal Government, including the more important work of saving and restoring our forests and the great improvement of waterways, are all proper government functions which must involve large expenditure if properly performed.”
—William Howard Taft (1857–1930)