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 great end of all human industry is the attainment of happiness. For this were arts invented, sciences cultivated, laws ordained, and societies modelled, by the most profound wisdom of patriots and legislators. Even the lonely savage, who lies exposed to the inclemency of the elements and the fury of wild beasts, forgets not, for a moment, this grand object of his being.”
—David Hume (1711–1776)
“There are laws for peace as well as war.”
—Titus Livius (Livy)
“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)