Conjunctive Normal Form

Discrete Mathematics: Conjunctive Normal Form
How to convert a Boolean Expression into Conjunctive Normal Form?
The Conjunctive Normal Form (CNF) is a standard form for representing logical formulas in propositional logic. In CNF, a formula is a conjunction (logical "and") of one or more clauses, where a clause is a disjunction (logical "or") of one or more literals.

For example, the formula (p ∧ ¬q) ∨ (q ∧ ¬r) can be written in CNF as (p ∨ q ∨ ¬r) ∧ (¬q ∨ p ∨ ¬r) ∧ (p ∨ ¬q ∨ r) ∧ (¬q ∨ ¬p ∨ r).

The CNF form is useful because it is a normal form, meaning that every formula in propositional logic can be converted into CNF. This makes it easier to manipulate formulas, especially for automated theorem proving and decision procedures.

CNF is also closely related to the concept of satisfiability (SAT), which is the problem of determining whether there exists an assignment of truth values to the variables of a formula that makes the formula true. The CNF form of a formula can be used to construct a boolean satisfiability problem, which can be solved efficiently using algorithms such as the Davis-Putnam algorithm.

In conclusion, the Conjunctive Normal Form is a standard form for representing logical formulas in propositional logic that is widely used in computer science and mathematics for its simplicity and efficient manipulation.
Higher Education Mathematics