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:
“If ... we admit a divinity, why not divine worship? and if worship, why not religion to teach this worship? and if a religion, why not the Christian, if a better cannot be assigned, and it be already established by the laws of our country, and handed down to us from our forefathers?”
—George Berkeley (1685–1753)
“The chess-board is the world; the pieces are the phenomena of the universe; the rules of the game are what we call the laws of Nature. The player on the other side is hidden from us. We know that his play is always fair, just, and patient. But also we know, to our cost, that he never overlooks a mistake, or makes the smallest allowance for ignorance.”
—Thomas Henry Huxley (1825–1895)
“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)