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 best laws cannot make a constitution work in spite of morals; morals can turn the worst laws to advantage. That is a commonplace truth, but one to which my studies are always bringing me back. It is the central point in my conception. I see it at the end of all my reflections.”
—Alexis de Tocqueville (1805–1859)
“The laws of custom make our [returning a visit] necessary. O how I hate this vile custom which obliges us to make slaves of ourselves! to sell the most precious property we boast, our time;—and to sacrifice it to every prattling impertinent who chooses to demand it!”
—Frances Burney (1752–1840)
“It ain’t no sin if you crack a few laws now and then, just so long as you don’t break any.”
—Mae West, U.S. actor, screenwriter, and A. Edward Sutherland. Peaches O’Day (Mae West)