2 Given the following formula F P Q P Q R R P Q Using only t

2. Given the following formula F:
(P Q) ((P Q ¬R) (R P Q))

Using only the equivalence transformations in Propositional Logic, prove that the ¬F is a contradiction.

3. Convert the following sentences to Conjunctive Normal Form (CNF).

3.1. ¬((¬P R) ((Q R) P))
3.2. ¬((P Q) ((P Q ¬R) (R P Q)))

3.3. ¬((P Q) (Q (P (P Q))))

3.4. (P Q) ((Q R) (P R))

Answer :

Given the following formula F :
(P Q) ((P Q ¬R) (R P Q))

(P Q) ((P Q) ( ¬R R )) Demorgan law

(P Q) ((P Q) ( F )) since ¬R R F

(P Q) (P Q) Since P V F P

¬ (P Q) V (P Q) since P V ¬ P T

Thus the given statement formula F is always true hance ¬ F is always false which is a contradiction..

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