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:
“... I want to live and be happy. I believe that we cannot be one or the other by pushing the absurd to all its consequences. I am like everyone. To feel liberated, I sometimes wish death on my loved ones, I covet the wives forbidden to me by the laws of family and friendship. To be logical, I should then kill or possess. But I judge that these vague ideas are unimportant. I everyone tried to put them to reality, we could neither live nor be happy.”
—Albert Camus (1913–1960)
“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 dangerous to tell the people that the laws are unjust; for they obey them only because they think them just. Therefore it is necessary to tell them at the same time that they must obey them because they are laws, just as they must obey superiors, not because they are just, but because they are superiors. In this way all sedition is prevented.”
—Blaise Pascal (1623–1662)