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:
“Between married persons, the cement of friendship is by the laws supposed so strong as to abolish all division of possessions: and has often, in reality, the force ascribed to it.
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—David Hume (1711–1776)
“Nothing is accidental in the universe—this is one of my Laws of Physics—except the entire universe itself, which is Pure Accident, pure divinity.”
—Joyce Carol Oates (b. 1938)
“The process of discovery is very simple. An unwearied and systematic application of known laws to nature causes the unknown to reveal themselves.”
—Henry David Thoreau (1817–1862)