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:
“Nearest to all things is that power which fashions their being. Next to us the grandest laws are constantly being executed. Next to us is not the workman whom we have hired, with whom we love so well to talk, but the workman whose work we are.”
—Henry David Thoreau (1817–1862)
“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)
“Our friendships hurry to short and poor conclusions, because we have made them a texture of wine and dreams, instead of the tough fibre of the human heart. The laws of friendship are austere and eternal, of one web with the laws of nature and of morals.”
—Ralph Waldo Emerson (1803–1882)