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 (logic)
Famous quotes containing the word laws:
“That man is a creature who needs order yet yearns for change is the creative contradiction at the heart of the laws which structure his conformity and define his deviancy.”
—Freda Adler (b. 1934)
“The best laws cannot make a constitution work in spite of morals; morals can turn the worst laws to advantage. That is a commonplace truth, but one to which my studies are always bringing me back. It is the central point in my conception. I see it at the end of all my reflections.”
—Alexis de Tocqueville (1805–1859)
“Sweet Cupid’s shafts, like destiny,
Doth causeless good or ill decree.
Desert is born out of his bow,
Reward upon his wing doth go.
What fools are they that have not known
That Love likes no laws but his own!”
—Fulke Greville (1554–1628)