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:
“The process of discovery is very simple. An unwearied and systematic application of known laws to nature causes the unknown to reveal themselves.”
—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)
“We agree fully that the mother and unborn child demand special consideration. But so does the soldier and the man maimed in industry. Industrial conditions that are suitable for a stalwart, young, unmarried woman are certainly not equally suitable to the pregnant woman or the mother of young children. Yet “welfare” laws apply to all women alike. Such blanket legislation is as absurd as fixing industrial conditions for men on a basis of their all being wounded soldiers would be.”
—National Woman’s Party, quoted in Everyone Was Brave. As, ch. 8, by William L. O’Neill (1969)