(p∧q)∨r
(p∧q∧(？ r∨r))∨((？ p∨p)∧(？ Q∨q)∧r) supplement.
((p∧q∧？ r)∨(p∧q∧r))∨((？ p∨p)∧(？ Q∨q)∧r) distribution law.
(p∧q∧？ r)∨(p∧q∧r)∨((？ p∨p)∧(？ Q∨q)∧r) associative law.
(p∧q∧？ r)∨(p∧q∧r)∨((？ p∧(？ q∨q)∧r)∨(p∧(？ Q∨q)∧r)) distribution law.
(p∧q∧？ r)∨(p∧q∧r)∨(？ p∧(？ q∨q)∧r)∨(p∧(？ Q∨q)∧r) associative law.
(p∧q∧？ r)∨(p∧q∧r)∨((？ p∧？ q∧r)∨(？ p∧q∧r))∨(p∧(？ Q∨q)∧r) distribution law.
(p∧q∧？ r)∨(p∧q∧r)∨(？ p∧？ q∧r)∨(？ p∧q∧r)∨(p∧(？ Q∨q)∧r) combination.
(p∧q∧？ r)∨(p∧q∧r)∨(？ p∧？ q∧r)∨(？ p∧q∧r)∨((p∧？ Q∧r)∨(p∧q∧r)) distribution law.
(p∧q∧？ r)∨(p∧q∧r)∨(？ p∧？ q∧r)∨(？ p∧q∧r)∨(p∧？ Q∧r)∨(p∧q∧r) associative law.
(p∧q∧？ r)∩(？ p∧？ q∧r)∨(？ p∧q∧r)∨(p∧？ The idempotent law of q∧r)∨(p∧q∧r).
Get the principal disjunctive normal form.
Extended data:
Disjunctive Paradigm and conjunctive normal form
Definition 2.2? Propositional variables and their negation are collectively called words. ? Disruption consisting of only a limited number of words is called simple disjunction.
A conjunctive form consisting of only a limited number of words is called a simple conjunctive form.
For example, words: p, ┐ q, r, q
Simple disjunction:? p,q,p∨q,p∨┐p∨r,┐p∨q∨┐r.
Simple conjunction:? p,┐r,┐p∧r,┐p∧q∧r,p∧q∧┐r.
Theorem 2. 1:
(1) Simple disjunction is tautology if and only if it contains a propositional variable and its negation.
(2) Simple conjunction is contradictory if and only if it contains a propositional variable and its negation.
Definition 2.3:
(1) The disjunctive form consisting of a finite number of simple conjunctions is called disjunctive paradigm.
(2) The conjunctive form consisting of finite simple disjunctions is called conjunctive normal form.
(3) Disjunctive paradigm and conjunctive normal form are collectively called paradigms.
For example, disjunctive paradigm: (p ┐∧ q) ∨ r, ┐ p ∨ q ∨ r, p ∨ q ∨ r.
Conjunctive normal form: (p ∨ q ∨ r) ∧ (∨ q ∨ r), p ∧ q ∧ r, P ∧ Q ∧ R.
Theorem 2.2:
(1) disjunctive normal form is contradictory if and only if every simple conjunction of it is contradictory.
Baidu encyclopedia-principal disjunctive paradigm