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Mathematical logic and foundations Definition

Disjunctive normal form

Definition

A literal is a propositional variable pp or its negation ¬p\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∧¬q)∨(q∧r)∨¬p(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.

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Further reading

  1. Web https://en.wikipedia.org/wiki/Disjunctive_normal_form, Definition
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