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
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It slipped from politics to puns,
It passed from Mahomet to Moses;
Beginning with the laws which keep
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And ending with some precept deep
For dressing eels, or shoeing horses.”
—Winthrop Mackworth Praed (1802–1839)
“As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.”
—Albert Einstein (1879–1955)
“It is the manners and spirit of a people which preserves a republic in vigour. A degeneracy in these is a canker which soon eats to the heart of its laws and constitution.”
—Thomas Jefferson (1743–1826)