Introduction

Having ten equivalences, nine common implications, and equivalences of propositional logic laws, please find three tasks to obtain the Conjunctive Normal Form (CNF) of the following propositional logic expressions.

Note: CNF is an AND of ORs (e.g. (P Q) (Q R))

Basic Logical Laws - Equivalences
Null Laws	P 0 0	P 1 1
Idempotent Laws	P P P	P P P
Involution Laws	(P) P	(P) P
Identity Laws	P 0 P	P 1 P
Negation Laws	P P 0	P P 1
Absorption Laws	P (P Q) P	P (P Q) P
De Morgan's Laws	(P Q) (P)(Q)	(P Q) (P) (Q)
Commutative Laws	P Q Q P	P Q Q P
Associative Laws	(P Q) R P (Q R)	(P Q) R P (Q R)
Distributive Laws	P (Q R) (P Q) (P R)	P (Q R) (P Q) (P R)

.

Basic logical laws - Common implications and equivalences
Disjunctive Addition	P (P Q)
Disjunctive Simplification	(P Q) P Q	(P Q) Q P
Conjunctive Simplification	(P Q) P	(P Q) Q
Contrapositive	(P Q) (Q P)
Conditional Equivalence	P Q P Q
Biconditional Equivalences	(P Q) (P Q) (Q P) (P Q) (P Q)
Chain Rule	(P Q) (Q R) (P R)
Indirect Reasoning (AKA Modus Tollens)	((P Q) Q P
Detachment (AKA Modus Ponens)	(P Q) P Q

Question to answer :

Example 3: Obtain the CNF for the following propositional logic expression:

P ((Q R))

Step 1
Step n
Result