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:
“Nearest to all things is that power which fashions their being. Next to us the grandest laws are constantly being executed. Next to us is not the workman whom we have hired, with whom we love so well to talk, but the workman whose work we are.”
—Henry David Thoreau (1817–1862)
“The main foundations of every state, new states as well as ancient or composite ones, are good laws and good arms ... you cannot have good laws without good arms, and where there are good arms, good laws inevitably follow.”
—Niccolò Machiavelli (1469–1527)
“Every individual, like a statue, develops in his life the laws of harmony, integrity, and freedom; or those of deformity, immorality, and bondage. Whether we wish to or not, we are all drawing our own pictures in the lives we are living ...”
—Harriot K. Hunt (1805–1875)