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:
“Language is a process of free creation; its laws and principles are fixed, but the manner in which the principles of generation are used is free and infinitely varied. Even the interpretation and use of words involves a process of free creation.”
—Noam Chomsky (b. 1928)
“I was not at all worried about finding my doctor boring; I expected from him, thanks to an art of which the laws escaped me, that he pronounce concerning my health an indisputable oracle by consulting my entrails.”
—Marcel Proust (1871–1922)
“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)