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:
“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)
“The tide which, after our former relaxed government, took a violent course towards the opposite extreme, and seemed ready to hang every thing round with the tassils and baubles of monarchy, is now getting back as we hope to a just mean, a government of laws addressed to the reason of the people, and not to their weaknesses.”
—Thomas Jefferson (1743–1826)
“The laws of Caesar are one thing, those of Christ, another. Papinianus judges one way, our Paul another.”
—Jerome (c. 340–420)