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:
“It is a base thing for a man among the people not to obey those in command. Never in a state can the laws be well administered when fear does not stand firm.”
—Sophocles (497–406/5 B.C.)
“Although philosophers generally believe in laws and deny causes, explanatory practice in physics is just the reverse.”
—Nancy Cartwright (b. 1945)
“One of the most attractive of those ancient books that I have met with is The Laws of Menu.”
—Henry David Thoreau (1817–1862)