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:
“Private property is held sacred in all good governments, and particularly in our own. Yet shall the fear of invading it prevent a general from marching his army over a cornfield or burning a house which protects the enemy? A thousand other instances might be cited to show that laws must sometimes be silent when necessity speaks.”
—Andrew Jackson (1767–1845)
“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)
“To know the laws is not to memorize their letter but to grasp their full force and meaning.”
—Marcus Tullius Cicero (106–43 B.C.)