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:
“The counting-room maxims liberally expounded are laws of the Universe. The merchant’s economy is a coarse symbol of the soul’s economy. It is, to spend for power, and not for pleasure.”
—Ralph Waldo Emerson (1803–1882)
“But while they prate of economic laws, men and women are starving. We must lay hold of the fact that economic laws are not made by nature. They are made by human beings.”
—Franklin D. Roosevelt (1882–1945)
“A pun is not bound by the laws which limit nicer wit. It is a pistol let off at the ear; not a feather to tickle the intellect.”
—Charles Lamb (1775–1834)