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 flatter myself [we] have in this country extinguished forever the ambitious hope of making laws for the human mind.”
—James Madison (1751–1836)
“Laws and customs may be creative of vice; and should be therefore perpetually under process of observation and correction: but laws and customs cannot be creative of virtue: they may encourage and help to preserve it; but they cannot originate it.”
—Harriet Martineau (1802–1876)
“While I am in favor of the Government promptly enforcing the laws for the present, defending the forts and collecting the revenue, I am not in favor of a war policy with a view to the conquest of any of the slave States; except such as are needed to give us a good boundary. If Maryland attempts to go off, suppress her in order to save the Potomac and the District of Columbia. Cut a piece off of western Virginia and keep Missouri and all the Territories.”
—Rutherford Birchard Hayes (1822–1893)