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:
“Nothing comes to pass in nature, which can be set down to a flaw therein; for nature is always the same and everywhere one and the same in her efficiency and power of action; that is, nature’s laws and ordinances whereby all things come to pass and change from one form to another, are everywhere and always; so that there should be one and the same method of understanding the nature of all things whatsoever, namely, through nature’s universal laws and rules.”
—Baruch (Benedict)
“Our books of science, as they improve in accuracy, are in danger of losing the freshness and vigor and readiness to appreciate the real laws of Nature, which is a marked merit in the ofttimes false theories of the ancients.”
—Henry David Thoreau (1817–1862)
“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)