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:
“... it is high time that the women of Republican America should know how much the laws that govern them are like the slave laws of the South ...”
—Harriot K. Hunt (1805–1875)
“What comes over a man, is it soul or mind
That to no limits and bounds he can stay confined?
You would say his ambition was to extend the reach
Clear to the Arctic of every living kind.
Why is his nature forever so hard to teach
That though there is no fixed line between wrong and right,
There are roughly zones whose laws must be obeyed?”
—Robert Frost (1874–1963)
“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)