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.
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Famous quotes containing the word laws:
“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)
“Our friendships hurry to short and poor conclusions, because we have made them a texture of wine and dreams, instead of the tough fibre of the human heart. The laws of friendship are austere and eternal, of one web with the laws of nature and of morals.”
—Ralph Waldo Emerson (1803–1882)
“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)