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:
“However great a man’s fear of life, suicide remains the courageous act, the clear- headed act of a mathematician. The suicide has judged by the laws of chance—so many odds against one that to live will be more miserable than to die. His sense of mathematics is greater than his sense of survival.”
—Graham Greene (1904–1991)
“I know not whether Laws be right
Or whether Laws be wrong;
All that we know who live in gaol
Is that the wall is strong;
And that each day is like a year,
A year whose days are long.”
—Oscar Wilde (1854–1900)
“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)