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)
“But while they prate of economic laws, men and women are starving. We must lay hold of the fact that economic laws are not made by nature. They are made by human beings.”
—Franklin D. Roosevelt (1882–1945)
“Always the laws of light are the same, but the modes and degrees of seeing vary.”
—Henry David Thoreau (1817–1862)