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:
“Let every American, every lover of liberty, every well wisher to his posterity, swear by the blood of the Revolution, never to violate in the least particular, the laws of the country; and never to tolerate their violation by others.”
—Abraham Lincoln (1809–1865)
“The new always happens against the overwhelming odds of statistical laws and their probability, which for all practical, everyday purposes amounts to certainty; the new therefore always appears in the guise of a miracle.”
—Hannah Arendt (1906–1975)
“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)