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:
“The laws of Caesar are one thing, those of Christ, another. Papinianus judges one way, our Paul another.”
—Jerome (c. 340–420)
“His talk was like a spring, which runs
With rapid change from rocks to roses:
It slipped from politics to puns,
It passed from Mahomet to Moses;
Beginning with the laws which keep
The planets in their radiant courses,
And ending with some precept deep
For dressing eels, or shoeing horses.”
—Winthrop Mackworth Praed (1802–1839)
“Nature and Nature’s laws lay hid in night;
God said Let Newton be! and all was light.”
—Alexander Pope (1688–1744)