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:
“What a pity if we do not live this short time according to the laws of the long time,—the eternal laws!”
—Henry David Thoreau (1817–1862)
“Every individual, like a statue, develops in his life the laws of harmony, integrity, and freedom; or those of deformity, immorality, and bondage. Whether we wish to or not, we are all drawing our own pictures in the lives we are living ...”
—Harriot K. Hunt (1805–1875)
“There are laws for peace as well as war.”
—Titus Livius (Livy)