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:
“Those rules of old discovered, not devised,
Are Nature sill, but Nature methodized;
Nature, like liberty, is but restrained
By the same laws which first herself ordained.”
—Alexander Pope (1688–1744)
“If ... we admit a divinity, why not divine worship? and if worship, why not religion to teach this worship? and if a religion, why not the Christian, if a better cannot be assigned, and it be already established by the laws of our country, and handed down to us from our forefathers?”
—George Berkeley (1685–1753)
“It is a power stronger than will.... Could a stone escape from the laws of gravity? Impossible. Impossible, for evil to form an alliance with good.”
—Isidore Ducasse, Comte de Lautréamont (1846–1870)