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:
“However great a man’s fear of life, suicide remains the courageous act, the clear- headed act of a mathematician. The suicide has judged by the laws of chance—so many odds against one that to live will be more miserable than to die. His sense of mathematics is greater than his sense of survival.”
—Graham Greene (1904–1991)
“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)
“At present the globe goes with a shattered constitution in its orbit.... No doubt the simple powers of nature, properly directed by man, would make it healthy and a paradise; as the laws of man’s own constitution but wait to be obeyed, to restore him to health and happiness.”
—Henry David Thoreau (1817–1862)