Question

Construct a formal proof of validity for the following argument. [10]

1. (N v O) → P

2. (P v Q) → R

3. Q v N

4. ¬ Q

∴ R

Answer 1

Let us construct a formal proof of validity from premises 1.- 4. to the conclusion $R$ using rules of inference :

$1.\ (N \lor O) → P\\$

$2.\ (P \lor Q) → R\\$

$3.\ Q \lor N\\$

$4.\ ¬ Q$

$5.\ N$ (using Disjunctive Syllogism to the premises 3. and 4.)

$6.\ N\lor O$ (using Disjunction Introduction to 5.)

$7.\ P$ (using Modus Ponens to 6. and 1.)

$8.\ P\lor Q$ (using Disjunction Introduction to 7.)

$9.\ R$ (using Modus Ponens to 8. and 2.)