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:
“These are not the artificial forests of an English king,—a royal preserve merely. Here prevail no forest laws but those of nature. The aborigines have never been dispossessed, nor nature disforested.”
—Henry David Thoreau (1817–1862)
“Sadder than destitution, sadder than a beggar is the man who eats alone in public. Nothing more contradicts the laws of man or beast, for animals always do each other the honor of sharing or disputing each other’s food.”
—Jean Baudrillard (b. 1929)
“The tide which, after our former relaxed government, took a violent course towards the opposite extreme, and seemed ready to hang every thing round with the tassils and baubles of monarchy, is now getting back as we hope to a just mean, a government of laws addressed to the reason of the people, and not to their weaknesses.”
—Thomas Jefferson (1743–1826)