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:
“I have no doubt but that the misery of the lower classes will be found to abate whenever the Government assumes a freer aspect and the laws favor a subdivision of Property.”
—James Madison (1751–1836)
“The Stage but echoes back the publick Voice.
The Drama’s Laws the Drama’s Patrons give,
For we that live to please, must please to live.”
—Samuel Johnson (1709–1784)
“It is a base thing for a man among the people not to obey those in command. Never in a state can the laws be well administered when fear does not stand firm.”
—Sophocles (497–406/5 B.C.)