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:
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—Elizabeth Cady Stanton (1815–1902)
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—William Cobbett (1762–1835)
“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)