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:
“All over this land women have no political existence. Laws pass over our heads that we can not unmake. Our property is taken from us without our consent. The babes we bear in anguish and carry in our arms are not ours.”
—Lucy Stone (1818–1893)
“If we are related, we shall meet. It was a tradition of the ancient world, that no metamorphosis could hide a god from a god; and there is a Greek verse which runs, “The Gods are to each other not unknown.” Friends also follow the laws of divine necessity; they gravitate to each other, and cannot otherwise.”
—Ralph Waldo Emerson (1803–1882)
“Our books of science, as they improve in accuracy, are in danger of losing the freshness and vigor and readiness to appreciate the real laws of Nature, which is a marked merit in the ofttimes false theories of the ancients.”
—Henry David Thoreau (1817–1862)