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 best laws cannot make a constitution work in spite of morals; morals can turn the worst laws to advantage. That is a commonplace truth, but one to which my studies are always bringing me back. It is the central point in my conception. I see it at the end of all my reflections.”
—Alexis de Tocqueville (1805–1859)
“One of the most attractive of those ancient books that I have met with is The Laws of Menu.”
—Henry David Thoreau (1817–1862)
“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)