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 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)
“Sweet Cupid’s shafts, like destiny,
Doth causeless good or ill decree.
Desert is born out of his bow,
Reward upon his wing doth go.
What fools are they that have not known
That Love likes no laws but his own!”
—Fulke Greville (1554–1628)
“The most mighty of nature’s laws is this, that out of Death she brings Life.”
—Herman Melville (1819–1891)