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:
“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)
“Although philosophers generally believe in laws and deny causes, explanatory practice in physics is just the reverse.”
—Nancy Cartwright (b. 1945)
“The laws of Caesar are one thing, those of Christ, another. Papinianus judges one way, our Paul another.”
—Jerome (c. 340–420)