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:
“We are told to maintain constitutions because they are constitutions, and what is laid down in those constitutions?... Certain great fundamental ideas of right are common to the world, and ... all laws of man’s making which trample on these ideas, are null and void—wrong to obey, right to disobey. The Constitution of the United States recognizes human slavery; and makes the souls of men articles of purchase and of sale.”
—Anna Elizabeth Dickinson (1842–1932)
“It is dangerous to tell the people that the laws are unjust; for they obey them only because they think them just. Therefore it is necessary to tell them at the same time that they must obey them because they are laws, just as they must obey superiors, not because they are just, but because they are superiors. In this way all sedition is prevented.”
—Blaise Pascal (1623–1662)
“At present the globe goes with a shattered constitution in its orbit.... No doubt the simple powers of nature, properly directed by man, would make it healthy and a paradise; as the laws of man’s own constitution but wait to be obeyed, to restore him to health and happiness.”
—Henry David Thoreau (1817–1862)