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 woman alone had suffered under these mistaken traditions [of women’s subordination], if she could have borne the evil by herself, it would have been less pitiful, but her brother man, in the laws he created and ignorantly worshipped, has suffered with her. He has lost her highest help; he has crippled the intelligence he needed; he has belittled the very source of his own being and dwarfed the image of his Maker.”
—Clara Barton (1821–1912)
“Our great Republic is a government of laws and not of men. Here, the people rule.”
—Gerald R. Ford (b. 1913)
“The more we learn of science, the more we see that its wonderful mysteries are all explained by a few simple laws so connected together and so dependent upon each other, that we see the same mind animating them all.”
—Olympia Brown (1835–1900)