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:
“There are laws for peace as well as war.”
—Titus Livius (Livy)
“We are told to maintain constitutions because they are constitutions, and what is laid down in those constitutions?... Certain great fundamental ideas of right are common to the world, and ... all laws of man’s making which trample on these ideas, are null and void—wrong to obey, right to disobey. The Constitution of the United States recognizes human slavery; and makes the souls of men articles of purchase and of sale.”
—Anna Elizabeth Dickinson (1842–1932)
“It is clear that in a monarchy, where he who commands the exceution of the laws generally thinks himself above them, there is less need of virtue than in a popular government, where the person entrusted with the execution of the laws is sensible of his being subject to their direction.”
—Charles Louis de Secondat Montesquieu (1689–1755)