Conjunctive Normal Form/Examples

Examples of Conjunctive Normal Form

$\paren {p \lor q} \land \paren {p \lor \neg r} \land \paren {q \lor r}$

is in CNF.

$\paren {\neg p \lor q \lor r} \land \paren {\paren {p \land \neg q} \lor r} \land \paren {\neg r}$

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

$\paren {\neg p \lor q \lor r} \land \neg \paren {\neg q \lor r} \land \paren {\neg r}$

is not in CNF because the second disjunction is negated.

$p \land q$

is in CNF, as it is a conjunction of literals.

$p \lor q$

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

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): conjunctive normal form