SE 500
Normal Forms (of Boolean Expressions)

Definition: A literal is a boolean variable, possibly negated. Examples: p, ¬q

Definition: A boolean expression is said to be in disjunctive normal form (DNF) if it has the form

E1 ∨ E2 ∨ ... ∨ En

where each Ei is a conjunction of (one or more) literals.

Example: (a ∧ ¬b ∧ c) ∨ (¬a ∧ b) ∨ (b ∧ ¬ c)

Definition: A boolean expression is said to be in conjunctive normal form (CNF) if it has the form

E1 ∧ E2 ∧ ... ∧ En

where each Ei is a disjunction of (one or more) literals.

Example: (a ∨ ¬b ∨ c) ∧ (¬a ∨ b) ∧ (b ∨ ¬ c)