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:
“Nothing is accidental in the universe—this is one of my Laws of Physics—except the entire universe itself, which is Pure Accident, pure divinity.”
—Joyce Carol Oates (b. 1938)
“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)
“Sadder than destitution, sadder than a beggar is the man who eats alone in public. Nothing more contradicts the laws of man or beast, for animals always do each other the honor of sharing or disputing each other’s food.”
—Jean Baudrillard (b. 1929)