Normal and Principle Forms Last Updated : 10 Mar, 2023 Improve Improve Like Article Like Save Share Report Disjunctive Normal Forms (DNF) : A formula which is equivalent to a given formula and which consists of a sum of elementary products is called a disjunctive normal form of given formula. Example : (P ∧ ~ Q) ∨ (Q ∧ R) ∨ (~ P ∧ Q ∧~ R) The DNF of formula is not unique. Conjunctive Normal Form (CNF) : A formula which is equivalent to a given formula and which consists of a product of elementary sums is called a conjunctive normal form of given formula. Example : (P~ ∨ Q) ∧ (Q ∨ R) ∧ (~ P ∨ Q ∨ ~ R) The CNF of formula is not unique. If every elementary sum in CNF is tautology, then given formula is also tautology. Principle Disjunctive Normal Form (PDNF) : An equivalent formula consisting of disjunctions of minterms only is called the principle disjunctive normal form of the formula. It is also known as sum-of-products canonical form. Example : (P ∧ ~ Q ∧ ~ R) ∨ (P ∧ ~ Q ∧ R) ∨ (~ P ∧ ~ Q ∧ ~ R) The minterm consists of conjunctions in which each statement variable or its negation, but not both, appears only once. The minterms are written down by including the variable if its truth value is T and its negation if its truth value is F. Principle Conjunctive Normal Form (PCNF) : An equivalent formula consisting of conjunctions of maxterms only is called the principle conjunctive normal form of the formula. It is also known as product-of-sums canonical form. Example : (P ∨ ~ Q ∨ ~ R) ∧ (P ∨ ~ Q ∨ R) ∧ (~ P ∨ ~ Q ∨ ~ R) The maxterm consists of disjunctions in which each variable or its negation, but not both, appears only once. The dual of a minterm is called a maxterm. Each of the maxterm has the truth value F for exactly one combination of the truth values of the variables. The maxterms are written down by including the variable if its truth value is F and its negation if its truth value is T. Like Article Suggest improvement Previous Mathematics | Classes (Injective, surjective, Bijective) of Functions Next Python - Central Limit Theorem Share your thoughts in the comments Add Your Comment Please Login to comment...