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:
“It is always a practical difficulty with clubs to regulate the laws of election so as to exclude peremptorily every social nuisance. Nobody wishes bad manners. We must have loyalty and character.”
—Ralph Waldo Emerson (1803–1882)
“While I am in favor of the Government promptly enforcing the laws for the present, defending the forts and collecting the revenue, I am not in favor of a war policy with a view to the conquest of any of the slave States; except such as are needed to give us a good boundary. If Maryland attempts to go off, suppress her in order to save the Potomac and the District of Columbia. Cut a piece off of western Virginia and keep Missouri and all the Territories.”
—Rutherford Birchard Hayes (1822–1893)
“Always the laws of light are the same, but the modes and degrees of seeing vary.”
—Henry David Thoreau (1817–1862)