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)
“The process of discovery is very simple. An unwearied and systematic application of known laws to nature causes the unknown to reveal themselves.”
—Henry David Thoreau (1817–1862)
“With a generous endowment of motherhood provided by legislation, with all laws against voluntary motherhood and education in its methods repealed, with the feminist ideal of education accepted in home and school, and with all special barriers removed in every field of human activity, there is no reason why woman should not become almost a human thing. It will be time enough then to consider whether she has a soul.”
—Crystal Eastman (1881–1928)