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 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)
“That man is a creature who needs order yet yearns for change is the creative contradiction at the heart of the laws which structure his conformity and define his deviancy.”
—Freda Adler (b. 1934)
“In time of war the laws are silent.”
—Marcus Tullius Cicero (106–43 B.C.)