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:
“That man is a creature who needs order yet yearns for change is the creative contradiction at the heart of the laws which structure his conformity and define his deviancy.”
—Freda Adler (b. 1934)
“Our books of science, as they improve in accuracy, are in danger of losing the freshness and vigor and readiness to appreciate the real laws of Nature, which is a marked merit in the ofttimes false theories of the ancients.”
—Henry David Thoreau (1817–1862)
“Laws and customs may be creative of vice; and should be therefore perpetually under process of observation and correction: but laws and customs cannot be creative of virtue: they may encourage and help to preserve it; but they cannot originate it.”
—Harriet Martineau (1802–1876)