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:
“A wise architect observed that you could break the laws of architectural art provided you had mastered them first. That would apply to religion as well as to art. Ignorance of the past does not guarantee freedom from its imperfections.”
—Reinhold Niebuhr (1892–1971)
“... it is high time that the women of Republican America should know how much the laws that govern them are like the slave laws of the South ...”
—Harriot K. Hunt (1805–1875)
“The most mighty of nature’s laws is this, that out of Death she brings Life.”
—Herman Melville (1819–1891)