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:
“There are laws for peace as well as war.”
—Titus Livius (Livy)
“I have not yet learned to live, that I can see, and I fear that I shall not very soon. I find, however, that in the long run things correspond to my original idea,—that they correspond to nothing else so much; and thus a man may really be a true prophet without any great exertion. The day is never so dark, nor the night even, but that the laws at least of light still prevail, and so may make it light in our minds if they are open to the truth.”
—Henry David Thoreau (1817–1862)
“His talk was like a spring, which runs
With rapid change from rocks to roses:
It slipped from politics to puns,
It passed from Mahomet to Moses;
Beginning with the laws which keep
The planets in their radiant courses,
And ending with some precept deep
For dressing eels, or shoeing horses.”
—Winthrop Mackworth Praed (1802–1839)