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)
“So far as laws and institutions avail, men should have equality of opportunity for happiness; that is, of education, wealth, power. These make happiness secure. An equal diffusion of happiness so far as laws and institutions avail.”
—Rutherford Birchard Hayes (1822–1893)
“Whenever there are in any country uncultivated lands and unemployed poor, it is clear that the laws of property have been so far extended as to violate natural right. The earth is given as a common stock for man to labor and live on.... The small landowners are the most precious part of a state.”
—Thomas Jefferson (1743–1826)