Lord conjunctive normal form: the conjunction of several largest terms.

Principal disjunction paradigm: disjunction of several minimum terms.

Conjunction: the same truth, the rest are false, which is equivalent to the intersection in the set;

Disjunction: taking truth from truth and taking falsehood from falsehood is equivalent to taking the union of sets.

Theorem:

(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:

(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.

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For example:

Example 1, find the principal disjunctive normal form and principal conjunctive normal form of formula (p ∧ q) ∨ r.

Main disjunctive paradigms:

(p∧q)∨r

& lt= = & gt(p∧q∧(r∨┐r))∨((p∨┐p)∧(q∨┐q)∧r)

& lt= = & gt(p∧q∧r)∨(p∧q∧┐r)∨(p∧q∧r)∨(p∧┐q∧r)∨(┐p∧q∧r)∨(┐p∧┐q∧r)

& lt= = & gt(p∧q∧r)∨(p∧q∧┐r)∨(p∧┐q∧r)∨(┐p∧q∧r)∨(┐p∧┐q∧r

Lord conjunctive normal form:

(p∧q)∨r

& lt= = & gt(p∨r)∧(q∨r)

& lt= = & gt(p∨(q∧┐q)∨r)∧((p∧┐p)∨q∨r)

& lt= = & gt(p∨q∨r)∧(p∨┐q∨r)∧(p∨q∨r)∧(┐p∨q∨r)

& lt= = & gt(p∨q∨r)∧(p∨┐q∨r)∧(┐p∨q∨r

From the above example, you can easily see the relationship between the two!

That is, a principal disjunctive normal form is transformed into a principal conjunctive normal form, that is, the maximum term of the label of the smallest term that does not exist in its principal disjunctive normal form is disjunctive, and vice versa!

Example 2, text: p, ┐ q, r, q

Simple disjunctions: p, q, p ∨ q, p ∨? p ∨ r, p ∨ q ∨ r.

Simple conjunctions: p, ┐ r, ┐ p ∧ r, ┐ p ∧ q ∧ r, p ∧ q ∧ q.

Summarize with your own hands and hope to adopt it!