Definition:Disjunctive Normal Form

Context
Propositional logic.

Definition
A logical formula $$P$$ is in disjunctive normal form (abbreviated DNF) if it consists of a disjunction of:
 * conjunctions of literals, and/or
 * literals,

Examples

 * $$\left({\neg p \and q \and r}\right) \or \left({\neg q \and r}\right) \or \left({\neg r}\right)$$

is in DNF.


 * $$\left({\neg p \and q \and r}\right) \or \left({\left({p \or \neg q}\right) \and r}\right) \or \left({\neg r}\right)$$

is not in DNF because there is a disjunction buried in the second conjunction.


 * $$\left({\neg p \and q \and r}\right) \or \neg \left({\neg q \and r}\right) \or \left({\neg r}\right)$$

is not in DNF because the second conjunction is negated.


 * $$p \or q$$

is in DNF, as it is a disjunction of literals.


 * $$p \and q$$

is in DNF, as it is a trivial (one-element) disjunction of a conjunction of literals.