Elementary Product Sum and Normal Forms

In this class, We discuss Elementary Product Sum and Normal Forms.

The reader should have prior knowledge of connectives and practice examples. Click here.

Elementary Product: The product of the variables and their negations in a formula is called an elementary product.

Examples: P, ¬P ∧ Q, ¬Q ∧ ¬P

Elementary Sum:

The sum of the variables and their negations in a formula is called an elementary sum.

Examples: P, ¬P ∨ Q, ¬Q ∨ ¬P

Normal Forms:

We have two normal forms

1) Disjunctive Normal Form

A formula equal to the given formula and consisting of the sum of elementary products is called disjunctive normal form.

Example:

(¬P ∧ Q) ∨ (P ∧ Q)

2) Conjunctive Normal Form

A formula equal to the given formula and consisting of the product of elementary sums is called conjunctive normal form.

Example:

(¬P ∨ Q) ∧ (P ∨ Q)