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)
“Surely it is one of the simplest laws of taste in dress, that it shall not attract undue attention from the wearer to the worn.”
—Elizabeth Stuart Phelps (1844–1911)
“The process of discovery is very simple. An unwearied and systematic application of known laws to nature causes the unknown to reveal themselves.”
—Henry David Thoreau (1817–1862)