What is the Full Form of DNF?

The full form of DNF is Disjunctive Normal Form.

Disjunctive Normal Form (DNF) is a standard normal form used in Boolean algebra and propositional logic. It is a logical formula expressed as a disjunction (OR) of one or more conjunctions (AND) of literals. A literal is a variable or its negation. Each conjunction is also known as a clause or a minterm.

Here's a breakdown:

• Disjunction: Represents the OR operation (symbol: ∨).
• Conjunction: Represents the AND operation (symbol: ∧).
• Literal: A propositional variable (e.g., p) or its negation (e.g., ¬p).

Example:

A propositional logic formula in DNF would look like this:

(A ∧ B) ∨ (¬A ∧ C) ∨ (B ∧ ¬C)

In this example:

• (A ∧ B), (¬A ∧ C), and (B ∧ ¬C) are the conjunctions or clauses.
• A, B, C, ¬A, and ¬C are the literals.
• The entire expression is a disjunction (OR) of these conjunctions.

k-DNF:

A k-DNF formula is a DNF formula where each conjunction contains exactly k literals.

Significance:

DNF is significant because any propositional logic formula can be converted into an equivalent DNF formula. This normal form is useful in automated theorem proving, circuit design, and other areas of computer science and logic.