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:
“To know the laws is not to memorize their letter but to grasp their full force and meaning.”
—Marcus Tullius Cicero (106–43 B.C.)
“So far as laws and institutions avail, men should have equality of opportunity for happiness; that is, of education, wealth, power. These make happiness secure. An equal diffusion of happiness so far as laws and institutions avail.”
—Rutherford Birchard Hayes (1822–1893)
“There are laws for peace as well as war.”
—Titus Livius (Livy)