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 members of a body-politic call it “the state” when it is passive, “the sovereign” when it is active, and a “power” when they compare it with others of its kind. Collectively they use the title “people,” and they refer to one another individually as “citizens” when speaking of their participation in the authority of the sovereign, and as “subjects” when speaking of their subordination to the laws of the state.”
—Jean-Jacques Rousseau (1712–1778)
“It is the manners and spirit of a people which preserves a republic in vigour. A degeneracy in these is a canker which soon eats to the heart of its laws and constitution.”
—Thomas Jefferson (1743–1826)
“Strange and predatory and truly dangerous, car thieves and muggers—they seem to jeopardize all our cherished concepts, even our self-esteem, our property rights, our powers of love, our laws and pleasures. The only relationship we seem to have with them is scorn or bewilderment, but they belong somewhere on the dark prairies of a country that is in the throes of self-discovery.”
—John Cheever (1912–1982)