# Normal Forms

**NORMAL FORMS**: Let us show how to find the formula given the Truth Table.

Formula obtained here is a “disjunction” of terms, each of which is a “conjunction” of “statement variables” and their “negations”. A product of statement variables and their negations is called “elementary production”. A sum of variables and their negations is called “elementary sum”.

** Disjunctive Nor mal Form**: A formula which is equivalent to a given formula and which has a sum of elementary products is called “disjunctive Normal Form” of the formula.

** Conjunctive Nor mal Form**: A formula which is equivalent to a given formula and that has a product of elementary sums is called “conjunctive Normal form” of the formula.

*Procedure to find disjunctive Normal form*

(ii) Using DeMorgan’s laws, an equivalent formula can be obtained in which the negation is applied to statement variables only, if the negation applied to a formula or part of the formula which is not a statement variable.

(iii) Applying the distributive law until a sum of elementary products is obtained.

This is the “Disjunctive Normal Form”, after applying the Idempotent law and suitable re-ordering. In the Normal Form, the elementary products which are equivalent to “F” (False), if any, can be ommitted.

**Example 1: **Obtain a disjunctive normal form of

**Solution:**