Disjunctive Normal Form

definitionlogic

Definition

A formula is in disjunctive normal form (DNF) if and only if it has the form,

$$({\ell }_{0,0}\wedge {\ell }_{0,1}\wedge \dots \wedge {\ell }_{0,i_0})\vee ({\ell }_{1,0}\wedge \dots \wedge {\ell }_{1,i_1})\vee \dots \vee ({\ell }_{k,0}\wedge \dots \wedge {\ell }_{k,i_k}).$$

Where ${\ell }_{a,b}$ is a literal.

Examples