Conjunctive Normal Form (CNF)


















What's Conjunctive Normal Form (or CNF)?

	a logic formula which is an 'and' (product) of clauses
	where each clause is an 'or' (sum) of literals

What's Disjunctive Normal Form (or DNF)?

	a logic formula which is an 'or' (sum) of terms
	where each term is an 'and' (product) of literals

What's a Literal?

	a single variable or a variable with a not applied to it

Which of the formulas are in Conjunctive Normal Form?

	(A or B) and (B -> C)
	(A or B or not C) and (not B or C)
	(A and B) or (not B and C or D)


















How do you convert a formula to CNF?

	1. remove -> and <->         (implication law)

	2. push NOTs                 (DeMorgans law)

	3. distribute ORs over ANDs  (distributive law)


















Give the algebraic steps for converting the formula to CNF.
Identify the algebraic law used in each step.


	(A or B) -> C


















Classwork

You may work with a partner.

Give the algebraic steps for converting the formula to CNF.
Identify the algebraic law used in each step.


	not (A and (B -> C))