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:
“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)
“The laws of God, the laws of man,
He may keep that will and can;
Not I: let God and man decree
Laws for themselves and not for me;”
—A.E. (Alfred Edward)
“I flatter myself [we] have in this country extinguished forever the ambitious hope of making laws for the human mind.”
—James Madison (1751–1836)