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:
“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)
“Nothing comes to pass in nature, which can be set down to a flaw therein; for nature is always the same and everywhere one and the same in her efficiency and power of action; that is, nature’s laws and ordinances whereby all things come to pass and change from one form to another, are everywhere and always; so that there should be one and the same method of understanding the nature of all things whatsoever, namely, through nature’s universal laws and rules.”
—Baruch (Benedict)
“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)