Editing Disjunctive normal form (section)

=== Remark ===
A propositional formula can be represented by one and only one full DNF.{{refn|name="noreps"|It is assumed that repetitions and variations<ref>like <math>(a \land b) \lor (b \land a) \lor (a \land b \land b)</math></ref> based on the [[Commutative property|commutativity]] and [[Associative property|associativity]] of <math>\lor</math> and <math>\land</math> do not occur.}} In contrast, several ''plain'' DNFs may be possible. For example, by applying the rule <math>((a \land b) \lor (\lnot a \land b)) \rightsquigarrow b</math> three times, the full DNF of the above <math>\phi</math> can be simplified to <math>(\lnot p \land \lnot q) \lor (\lnot p \land r) \lor (\lnot q \land r)</math>. However, there are also equivalent DNF formulas that cannot be transformed one into another by this rule, see the pictures for an example.