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 little profits that an idle king,
By this still hearth, among these barren crags,
Matched with an aged wife, I mete and dole
Unequal laws unto a savage race
That hoard, and sleep, and feed,”
—Alfred Tennyson (1809–1892)
“The life of a good man will hardly improve us more than the life of a freebooter, for the inevitable laws appear as plainly in the infringement as in the observance, and our lives are sustained by a nearly equal expense of virtue of some kind. The decaying tree, while yet it lives, demands sun, wind, and rain no less than the green one. It secretes sap and performs the functions of health. If we choose, we may study the alburnum only. The gnarled stump has as tender a bud as the sapling.”
—Henry David Thoreau (1817–1862)
“The members of a body-politic call it “the state” when it is passive, “the sovereign” when it is active, and a “power” when they compare it with others of its kind. Collectively they use the title “people,” and they refer to one another individually as “citizens” when speaking of their participation in the authority of the sovereign, and as “subjects” when speaking of their subordination to the laws of the state.”
—Jean-Jacques Rousseau (1712–1778)