Disjunctive normal form

Definition

A literal is a propositional variable $p$ or its negation $\neg p$. A formula of propositional logic is in disjunctive normal form if it is a disjunction of one or more conjunctions of one or more literals.

Remarks

Example: $(p \wedge \neg q) \vee (q \wedge r) \vee \neg p$ is in disjunctive normal form. Every formula is logically equivalent to a formula in disjunctive normal form. For a formula that is not a contradiction, take one conjunction for each row of the truth table where it is true. A consequence: the connectives $\wedge$, $\vee$ and $\neg$ are functionally complete.

Explanations

L1 human

A formula in disjunctive normal form is an or of ands of simple conditions. It lists all the cases in which the formula is true.